diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..dfe0770 --- /dev/null +++ b/.gitattributes @@ -0,0 +1,2 @@ +# Auto detect text files and perform LF normalization +* text=auto diff --git a/.gitignore b/.gitignore index 4a4940a..7eff386 100644 --- a/.gitignore +++ b/.gitignore @@ -3,6 +3,8 @@ Uniform Distribution.ipynb основы статистики.ipynb -.ipynb_checkpoints/конспект-checkpoint.ipynb - .ipynb_checkpoints/ +*.ipynb_checkpoints/ +.ipynb_checkpoints/** + +.venv diff --git a/README.md b/README.md index 6ce27e9..e44ffc3 100644 --- a/README.md +++ b/README.md @@ -1,12 +1,20 @@ # Основы статистики - -все объёмный конспект [лекций ](https://stepik.org/course/76) +## Описание +Форк от [GitHub репозитория](https://github.com/KlukvaMors/basic_stat) объёмного конспекта [лекций](https://stepik.org/course/76). +Кое-где исправлены опечатки, кое-где добавлен конспект и код на python, кое-где сделаны косметические изменения на мой вкус. Автор лекций: **Anatoliy Karpov** ![Saint_Karpov](img/Saint_Karpov.png) +Конспект сопровождается кодом на python 3 с использованием Jupyter Notebook для демонстрации или решения предложенных в курсе лекций задач. +## Запуск +Для установки нужных модулей python через менеджер `pip` выполните в темринале из директории со скаченным репозиторием следующую команду +``` bash +pip install -r requirements.txt +``` +## Примечание Так как рендер ноутбуков от гитхаб грубоват, то читать лекции удобнее от [сюда ](https://nbviewer.jupyter.org/github/KlukvaMors/basic_stat/blob/main/конспект.ipynb?flush_cache=true) diff --git a/data/atherosclerosis.csv b/data/atherosclerosis.csv new file mode 100644 index 0000000..27b8acc --- /dev/null +++ b/data/atherosclerosis.csv @@ -0,0 +1,65 @@ +"expr","age","dose" +107.351478054914,"1","D1" +104.504438134304,"1","D1" +103.435134210494,"1","D1" +109.572882092261,"1","D1" +114.99380251712,"1","D1" +106.060605357622,"1","D1" +114.593613086389,"1","D1" 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Laina female 26 0 0 STON/O2. 3101282 7.925 S +4 1 1 Futrelle, Mrs. Jacques Heath (Lily May Peel) female 35 1 0 113803 53.1 C123 S +5 0 3 Allen, Mr. William Henry male 35 0 0 373450 8.05 S +6 0 3 Moran, Mr. James male 0 0 330877 8.4583 Q +7 0 1 McCarthy, Mr. Timothy J male 54 0 0 17463 51.8625 E46 S +8 0 3 Palsson, Master. Gosta Leonard male 2 3 1 349909 21.075 S +9 1 3 Johnson, Mrs. Oscar W (Elisabeth Vilhelmina Berg) female 27 0 2 347742 11.1333 S +10 1 2 Nasser, Mrs. Nicholas (Adele Achem) female 14 1 0 237736 30.0708 C +11 1 3 Sandstrom, Miss. Marguerite Rut female 4 1 1 PP 9549 16.7 G6 S +12 1 1 Bonnell, Miss. Elizabeth female 58 0 0 113783 26.55 C103 S +13 0 3 Saundercock, Mr. William Henry male 20 0 0 A/5. 2151 8.05 S +14 0 3 Andersson, Mr. Anders Johan male 39 1 5 347082 31.275 S +15 0 3 Vestrom, Miss. Hulda Amanda Adolfina female 14 0 0 350406 7.8542 S +16 1 2 Hewlett, Mrs. (Mary D Kingcome) female 55 0 0 248706 16 S +17 0 3 Rice, Master. Eugene male 2 4 1 382652 29.125 Q +18 1 2 Williams, Mr. Charles Eugene male 0 0 244373 13 S +19 0 3 Vander Planke, Mrs. Julius (Emelia Maria Vandemoortele) female 31 1 0 345763 18 S +20 1 3 Masselmani, Mrs. Fatima female 0 0 2649 7.225 C +21 0 2 Fynney, Mr. Joseph J male 35 0 0 239865 26 S +22 1 2 Beesley, Mr. Lawrence male 34 0 0 248698 13 D56 S +23 1 3 "McGowan, Miss. Anna ""Annie""" female 15 0 0 330923 8.0292 Q +24 1 1 Sloper, Mr. William Thompson male 28 0 0 113788 35.5 A6 S +25 0 3 Palsson, Miss. Torborg Danira female 8 3 1 349909 21.075 S +26 1 3 Asplund, Mrs. Carl Oscar (Selma Augusta Emilia Johansson) female 38 1 5 347077 31.3875 S +27 0 3 Emir, Mr. Farred Chehab male 0 0 2631 7.225 C +28 0 1 Fortune, Mr. Charles Alexander male 19 3 2 19950 263 C23 C25 C27 S +29 1 3 "O'Dwyer, Miss. Ellen ""Nellie""" female 0 0 330959 7.8792 Q +30 0 3 Todoroff, Mr. Lalio male 0 0 349216 7.8958 S +31 0 1 Uruchurtu, Don. Manuel E male 40 0 0 PC 17601 27.7208 C +32 1 1 Spencer, Mrs. William Augustus (Marie Eugenie) female 1 0 PC 17569 146.5208 B78 C +33 1 3 Glynn, Miss. Mary Agatha female 0 0 335677 7.75 Q +34 0 2 Wheadon, Mr. Edward H male 66 0 0 C.A. 24579 10.5 S +35 0 1 Meyer, Mr. Edgar Joseph male 28 1 0 PC 17604 82.1708 C +36 0 1 Holverson, Mr. Alexander Oskar male 42 1 0 113789 52 S +37 1 3 Mamee, Mr. Hanna male 0 0 2677 7.2292 C +38 0 3 Cann, Mr. Ernest Charles male 21 0 0 A./5. 2152 8.05 S +39 0 3 Vander Planke, Miss. Augusta Maria female 18 2 0 345764 18 S +40 1 3 Nicola-Yarred, Miss. Jamila female 14 1 0 2651 11.2417 C +41 0 3 Ahlin, Mrs. Johan (Johanna Persdotter Larsson) female 40 1 0 7546 9.475 S +42 0 2 Turpin, Mrs. William John Robert (Dorothy Ann Wonnacott) female 27 1 0 11668 21 S +43 0 3 Kraeff, Mr. Theodor male 0 0 349253 7.8958 C +44 1 2 Laroche, Miss. Simonne Marie Anne Andree female 3 1 2 SC/Paris 2123 41.5792 C +45 1 3 Devaney, Miss. Margaret Delia female 19 0 0 330958 7.8792 Q +46 0 3 Rogers, Mr. William John male 0 0 S.C./A.4. 23567 8.05 S +47 0 3 Lennon, Mr. Denis male 1 0 370371 15.5 Q +48 1 3 O'Driscoll, Miss. Bridget female 0 0 14311 7.75 Q +49 0 3 Samaan, Mr. Youssef male 2 0 2662 21.6792 C +50 0 3 Arnold-Franchi, Mrs. Josef (Josefine Franchi) female 18 1 0 349237 17.8 S +51 0 3 Panula, Master. Juha Niilo male 7 4 1 3101295 39.6875 S +52 0 3 Nosworthy, Mr. Richard Cater male 21 0 0 A/4. 39886 7.8 S +53 1 1 Harper, Mrs. Henry Sleeper (Myna Haxtun) female 49 1 0 PC 17572 76.7292 D33 C +54 1 2 Faunthorpe, Mrs. Lizzie (Elizabeth Anne Wilkinson) female 29 1 0 2926 26 S +55 0 1 Ostby, Mr. Engelhart Cornelius male 65 0 1 113509 61.9792 B30 C +56 1 1 Woolner, Mr. Hugh male 0 0 19947 35.5 C52 S +57 1 2 Rugg, Miss. Emily female 21 0 0 C.A. 31026 10.5 S +58 0 3 Novel, Mr. Mansouer male 28.5 0 0 2697 7.2292 C +59 1 2 West, Miss. Constance Mirium female 5 1 2 C.A. 34651 27.75 S +60 0 3 Goodwin, Master. William Frederick male 11 5 2 CA 2144 46.9 S +61 0 3 Sirayanian, Mr. Orsen male 22 0 0 2669 7.2292 C +62 1 1 Icard, Miss. Amelie female 38 0 0 113572 80 B28 +63 0 1 Harris, Mr. Henry Birkhardt male 45 1 0 36973 83.475 C83 S +64 0 3 Skoog, Master. Harald male 4 3 2 347088 27.9 S +65 0 1 Stewart, Mr. Albert A male 0 0 PC 17605 27.7208 C +66 1 3 Moubarek, Master. Gerios male 1 1 2661 15.2458 C +67 1 2 Nye, Mrs. (Elizabeth Ramell) female 29 0 0 C.A. 29395 10.5 F33 S +68 0 3 Crease, Mr. Ernest James male 19 0 0 S.P. 3464 8.1583 S +69 1 3 Andersson, Miss. Erna Alexandra female 17 4 2 3101281 7.925 S +70 0 3 Kink, Mr. Vincenz male 26 2 0 315151 8.6625 S +71 0 2 Jenkin, Mr. Stephen Curnow male 32 0 0 C.A. 33111 10.5 S +72 0 3 Goodwin, Miss. 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Bertha female 17 0 0 SO/C 14885 10.5 S +86 1 3 Backstrom, Mrs. Karl Alfred (Maria Mathilda Gustafsson) female 33 3 0 3101278 15.85 S +87 0 3 Ford, Mr. William Neal male 16 1 3 W./C. 6608 34.375 S +88 0 3 Slocovski, Mr. Selman Francis male 0 0 SOTON/OQ 392086 8.05 S +89 1 1 Fortune, Miss. Mabel Helen female 23 3 2 19950 263 C23 C25 C27 S +90 0 3 Celotti, Mr. Francesco male 24 0 0 343275 8.05 S +91 0 3 Christmann, Mr. Emil male 29 0 0 343276 8.05 S +92 0 3 Andreasson, Mr. Paul Edvin male 20 0 0 347466 7.8542 S +93 0 1 Chaffee, Mr. Herbert Fuller male 46 1 0 W.E.P. 5734 61.175 E31 S +94 0 3 Dean, Mr. Bertram Frank male 26 1 2 C.A. 2315 20.575 S +95 0 3 Coxon, Mr. Daniel male 59 0 0 364500 7.25 S +96 0 3 Shorney, Mr. Charles Joseph male 0 0 374910 8.05 S +97 0 1 Goldschmidt, Mr. George B male 71 0 0 PC 17754 34.6542 A5 C +98 1 1 Greenfield, Mr. William Bertram male 23 0 1 PC 17759 63.3583 D10 D12 C +99 1 2 Doling, Mrs. John T (Ada Julia Bone) female 34 0 1 231919 23 S +100 0 2 Kantor, Mr. Sinai male 34 1 0 244367 26 S +101 0 3 Petranec, Miss. 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Anna female 1 1 2668 22.3583 F E69 C +130 0 3 Ekstrom, Mr. Johan male 45 0 0 347061 6.975 S +131 0 3 Drazenoic, Mr. Jozef male 33 0 0 349241 7.8958 C +132 0 3 Coelho, Mr. Domingos Fernandeo male 20 0 0 SOTON/O.Q. 3101307 7.05 S +133 0 3 Robins, Mrs. Alexander A (Grace Charity Laury) female 47 1 0 A/5. 3337 14.5 S +134 1 2 Weisz, Mrs. Leopold (Mathilde Francoise Pede) female 29 1 0 228414 26 S +135 0 2 Sobey, Mr. Samuel James Hayden male 25 0 0 C.A. 29178 13 S +136 0 2 Richard, Mr. Emile male 23 0 0 SC/PARIS 2133 15.0458 C +137 1 1 Newsom, Miss. Helen Monypeny female 19 0 2 11752 26.2833 D47 S +138 0 1 Futrelle, Mr. Jacques Heath male 37 1 0 113803 53.1 C123 S +139 0 3 Osen, Mr. Olaf Elon male 16 0 0 7534 9.2167 S +140 0 1 Giglio, Mr. Victor male 24 0 0 PC 17593 79.2 B86 C +141 0 3 Boulos, Mrs. Joseph (Sultana) female 0 2 2678 15.2458 C +142 1 3 Nysten, Miss. Anna Sofia female 22 0 0 347081 7.75 S +143 1 3 Hakkarainen, Mrs. Pekka Pietari (Elin Matilda Dolck) female 24 1 0 STON/O2. 3101279 15.85 S +144 0 3 Burke, Mr. Jeremiah male 19 0 0 365222 6.75 Q +145 0 2 Andrew, Mr. Edgardo Samuel male 18 0 0 231945 11.5 S +146 0 2 Nicholls, Mr. Joseph Charles male 19 1 1 C.A. 33112 36.75 S +147 1 3 "Andersson, Mr. August Edvard (""Wennerstrom"")" male 27 0 0 350043 7.7958 S +148 0 3 "Ford, Miss. Robina Maggie ""Ruby""" female 9 2 2 W./C. 6608 34.375 S +149 0 2 "Navratil, Mr. Michel (""Louis M Hoffman"")" male 36.5 0 2 230080 26 F2 S +150 0 2 Byles, Rev. Thomas Roussel Davids male 42 0 0 244310 13 S +151 0 2 Bateman, Rev. Robert James male 51 0 0 S.O.P. 1166 12.525 S +152 1 1 Pears, Mrs. Thomas (Edith Wearne) female 22 1 0 113776 66.6 C2 S +153 0 3 Meo, Mr. Alfonzo male 55.5 0 0 A.5. 11206 8.05 S +154 0 3 van Billiard, Mr. Austin Blyler male 40.5 0 2 A/5. 851 14.5 S +155 0 3 Olsen, Mr. Ole Martin male 0 0 Fa 265302 7.3125 S +156 0 1 Williams, Mr. Charles Duane male 51 0 1 PC 17597 61.3792 C +157 1 3 "Gilnagh, Miss. Katherine ""Katie""" female 16 0 0 35851 7.7333 Q +158 0 3 Corn, Mr. Harry male 30 0 0 SOTON/OQ 392090 8.05 S +159 0 3 Smiljanic, Mr. Mile male 0 0 315037 8.6625 S +160 0 3 Sage, Master. Thomas Henry male 8 2 CA. 2343 69.55 S +161 0 3 Cribb, Mr. John Hatfield male 44 0 1 371362 16.1 S +162 1 2 "Watt, Mrs. James (Elizabeth ""Bessie"" Inglis Milne)" female 40 0 0 C.A. 33595 15.75 S +163 0 3 Bengtsson, Mr. John Viktor male 26 0 0 347068 7.775 S +164 0 3 Calic, Mr. Jovo male 17 0 0 315093 8.6625 S +165 0 3 Panula, Master. Eino Viljami male 1 4 1 3101295 39.6875 S +166 1 3 "Goldsmith, Master. Frank John William ""Frankie""" male 9 0 2 363291 20.525 S +167 1 1 Chibnall, Mrs. (Edith Martha Bowerman) female 0 1 113505 55 E33 S +168 0 3 Skoog, Mrs. William (Anna Bernhardina Karlsson) female 45 1 4 347088 27.9 S +169 0 1 Baumann, Mr. John D male 0 0 PC 17318 25.925 S +170 0 3 Ling, Mr. Lee male 28 0 0 1601 56.4958 S +171 0 1 Van der hoef, Mr. Wyckoff male 61 0 0 111240 33.5 B19 S +172 0 3 Rice, Master. Arthur male 4 4 1 382652 29.125 Q +173 1 3 Johnson, Miss. Eleanor Ileen female 1 1 1 347742 11.1333 S +174 0 3 Sivola, Mr. Antti Wilhelm male 21 0 0 STON/O 2. 3101280 7.925 S +175 0 1 Smith, Mr. James Clinch male 56 0 0 17764 30.6958 A7 C +176 0 3 Klasen, Mr. Klas Albin male 18 1 1 350404 7.8542 S +177 0 3 Lefebre, Master. Henry Forbes male 3 1 4133 25.4667 S +178 0 1 Isham, Miss. Ann Elizabeth female 50 0 0 PC 17595 28.7125 C49 C +179 0 2 Hale, Mr. Reginald male 30 0 0 250653 13 S +180 0 3 Leonard, Mr. Lionel male 36 0 0 LINE 0 S +181 0 3 Sage, Miss. Constance Gladys female 8 2 CA. 2343 69.55 S +182 0 2 Pernot, Mr. Rene male 0 0 SC/PARIS 2131 15.05 C +183 0 3 Asplund, Master. Clarence Gustaf Hugo male 9 4 2 347077 31.3875 S +184 1 2 Becker, Master. Richard F male 1 2 1 230136 39 F4 S +185 1 3 Kink-Heilmann, Miss. Luise Gretchen female 4 0 2 315153 22.025 S +186 0 1 Rood, Mr. Hugh Roscoe male 0 0 113767 50 A32 S +187 1 3 "O'Brien, Mrs. Thomas (Johanna ""Hannah"" Godfrey)" female 1 0 370365 15.5 Q +188 1 1 "Romaine, Mr. Charles Hallace (""Mr C Rolmane"")" male 45 0 0 111428 26.55 S +189 0 3 Bourke, Mr. John male 40 1 1 364849 15.5 Q +190 0 3 Turcin, Mr. Stjepan male 36 0 0 349247 7.8958 S +191 1 2 Pinsky, Mrs. (Rosa) female 32 0 0 234604 13 S +192 0 2 Carbines, Mr. William male 19 0 0 28424 13 S +193 1 3 Andersen-Jensen, Miss. Carla Christine Nielsine female 19 1 0 350046 7.8542 S +194 1 2 Navratil, Master. Michel M male 3 1 1 230080 26 F2 S +195 1 1 Brown, Mrs. James Joseph (Margaret Tobin) female 44 0 0 PC 17610 27.7208 B4 C +196 1 1 Lurette, Miss. Elise female 58 0 0 PC 17569 146.5208 B80 C +197 0 3 Mernagh, Mr. Robert male 0 0 368703 7.75 Q +198 0 3 Olsen, Mr. Karl Siegwart Andreas male 42 0 1 4579 8.4042 S +199 1 3 "Madigan, Miss. Margaret ""Maggie""" female 0 0 370370 7.75 Q +200 0 2 "Yrois, Miss. Henriette (""Mrs Harbeck"")" female 24 0 0 248747 13 S +201 0 3 Vande Walle, Mr. Nestor Cyriel male 28 0 0 345770 9.5 S +202 0 3 Sage, Mr. Frederick male 8 2 CA. 2343 69.55 S +203 0 3 Johanson, Mr. Jakob Alfred male 34 0 0 3101264 6.4958 S +204 0 3 Youseff, Mr. Gerious male 45.5 0 0 2628 7.225 C +205 1 3 "Cohen, Mr. Gurshon ""Gus""" male 18 0 0 A/5 3540 8.05 S +206 0 3 Strom, Miss. Telma Matilda female 2 0 1 347054 10.4625 G6 S +207 0 3 Backstrom, Mr. Karl Alfred male 32 1 0 3101278 15.85 S +208 1 3 Albimona, Mr. Nassef Cassem male 26 0 0 2699 18.7875 C +209 1 3 "Carr, Miss. Helen ""Ellen""" female 16 0 0 367231 7.75 Q +210 1 1 Blank, Mr. Henry male 40 0 0 112277 31 A31 C +211 0 3 Ali, Mr. Ahmed male 24 0 0 SOTON/O.Q. 3101311 7.05 S +212 1 2 Cameron, Miss. Clear Annie female 35 0 0 F.C.C. 13528 21 S +213 0 3 Perkin, Mr. John Henry male 22 0 0 A/5 21174 7.25 S +214 0 2 Givard, Mr. Hans Kristensen male 30 0 0 250646 13 S +215 0 3 Kiernan, Mr. Philip male 1 0 367229 7.75 Q +216 1 1 Newell, Miss. Madeleine female 31 1 0 35273 113.275 D36 C +217 1 3 Honkanen, Miss. Eliina female 27 0 0 STON/O2. 3101283 7.925 S +218 0 2 Jacobsohn, Mr. Sidney Samuel male 42 1 0 243847 27 S +219 1 1 Bazzani, Miss. Albina female 32 0 0 11813 76.2917 D15 C +220 0 2 Harris, Mr. Walter male 30 0 0 W/C 14208 10.5 S +221 1 3 Sunderland, Mr. Victor Francis male 16 0 0 SOTON/OQ 392089 8.05 S +222 0 2 Bracken, Mr. James H male 27 0 0 220367 13 S +223 0 3 Green, Mr. George Henry male 51 0 0 21440 8.05 S +224 0 3 Nenkoff, Mr. Christo male 0 0 349234 7.8958 S +225 1 1 Hoyt, Mr. Frederick Maxfield male 38 1 0 19943 90 C93 S +226 0 3 Berglund, Mr. Karl Ivar Sven male 22 0 0 PP 4348 9.35 S +227 1 2 Mellors, Mr. William John male 19 0 0 SW/PP 751 10.5 S +228 0 3 "Lovell, Mr. John Hall (""Henry"")" male 20.5 0 0 A/5 21173 7.25 S +229 0 2 Fahlstrom, Mr. Arne Jonas male 18 0 0 236171 13 S +230 0 3 Lefebre, Miss. Mathilde female 3 1 4133 25.4667 S +231 1 1 Harris, Mrs. Henry Birkhardt (Irene Wallach) female 35 1 0 36973 83.475 C83 S +232 0 3 Larsson, Mr. Bengt Edvin male 29 0 0 347067 7.775 S +233 0 2 Sjostedt, Mr. Ernst Adolf male 59 0 0 237442 13.5 S +234 1 3 Asplund, Miss. Lillian Gertrud female 5 4 2 347077 31.3875 S +235 0 2 Leyson, Mr. Robert William Norman male 24 0 0 C.A. 29566 10.5 S +236 0 3 Harknett, Miss. Alice Phoebe female 0 0 W./C. 6609 7.55 S +237 0 2 Hold, Mr. Stephen male 44 1 0 26707 26 S +238 1 2 "Collyer, Miss. Marjorie ""Lottie""" female 8 0 2 C.A. 31921 26.25 S +239 0 2 Pengelly, Mr. Frederick William male 19 0 0 28665 10.5 S +240 0 2 Hunt, Mr. George Henry male 33 0 0 SCO/W 1585 12.275 S +241 0 3 Zabour, Miss. Thamine female 1 0 2665 14.4542 C +242 1 3 "Murphy, Miss. Katherine ""Kate""" female 1 0 367230 15.5 Q +243 0 2 Coleridge, Mr. Reginald Charles male 29 0 0 W./C. 14263 10.5 S +244 0 3 Maenpaa, Mr. Matti Alexanteri male 22 0 0 STON/O 2. 3101275 7.125 S +245 0 3 Attalah, Mr. Sleiman male 30 0 0 2694 7.225 C +246 0 1 Minahan, Dr. William Edward male 44 2 0 19928 90 C78 Q +247 0 3 Lindahl, Miss. Agda Thorilda Viktoria female 25 0 0 347071 7.775 S +248 1 2 Hamalainen, Mrs. William (Anna) female 24 0 2 250649 14.5 S +249 1 1 Beckwith, Mr. Richard Leonard male 37 1 1 11751 52.5542 D35 S +250 0 2 Carter, Rev. Ernest Courtenay male 54 1 0 244252 26 S +251 0 3 Reed, Mr. James George male 0 0 362316 7.25 S +252 0 3 Strom, Mrs. Wilhelm (Elna Matilda Persson) female 29 1 1 347054 10.4625 G6 S +253 0 1 Stead, Mr. William Thomas male 62 0 0 113514 26.55 C87 S +254 0 3 Lobb, Mr. William Arthur male 30 1 0 A/5. 3336 16.1 S +255 0 3 Rosblom, Mrs. Viktor (Helena Wilhelmina) female 41 0 2 370129 20.2125 S +256 1 3 Touma, Mrs. Darwis (Hanne Youssef Razi) female 29 0 2 2650 15.2458 C +257 1 1 Thorne, Mrs. Gertrude Maybelle female 0 0 PC 17585 79.2 C +258 1 1 Cherry, Miss. Gladys female 30 0 0 110152 86.5 B77 S +259 1 1 Ward, Miss. Anna female 35 0 0 PC 17755 512.3292 C +260 1 2 Parrish, Mrs. (Lutie Davis) female 50 0 1 230433 26 S +261 0 3 Smith, Mr. Thomas male 0 0 384461 7.75 Q +262 1 3 Asplund, Master. Edvin Rojj Felix male 3 4 2 347077 31.3875 S +263 0 1 Taussig, Mr. Emil male 52 1 1 110413 79.65 E67 S +264 0 1 Harrison, Mr. William male 40 0 0 112059 0 B94 S +265 0 3 Henry, Miss. Delia female 0 0 382649 7.75 Q +266 0 2 Reeves, Mr. David male 36 0 0 C.A. 17248 10.5 S +267 0 3 Panula, Mr. Ernesti Arvid male 16 4 1 3101295 39.6875 S +268 1 3 Persson, Mr. Ernst Ulrik male 25 1 0 347083 7.775 S +269 1 1 Graham, Mrs. William Thompson (Edith Junkins) female 58 0 1 PC 17582 153.4625 C125 S +270 1 1 Bissette, Miss. Amelia female 35 0 0 PC 17760 135.6333 C99 S +271 0 1 Cairns, Mr. Alexander male 0 0 113798 31 S +272 1 3 Tornquist, Mr. William Henry male 25 0 0 LINE 0 S +273 1 2 Mellinger, Mrs. (Elizabeth Anne Maidment) female 41 0 1 250644 19.5 S +274 0 1 Natsch, Mr. Charles H male 37 0 1 PC 17596 29.7 C118 C +275 1 3 "Healy, Miss. Hanora ""Nora""" female 0 0 370375 7.75 Q +276 1 1 Andrews, Miss. Kornelia Theodosia female 63 1 0 13502 77.9583 D7 S +277 0 3 Lindblom, Miss. Augusta Charlotta female 45 0 0 347073 7.75 S +278 0 2 "Parkes, Mr. Francis ""Frank""" male 0 0 239853 0 S +279 0 3 Rice, Master. Eric male 7 4 1 382652 29.125 Q +280 1 3 Abbott, Mrs. Stanton (Rosa Hunt) female 35 1 1 C.A. 2673 20.25 S +281 0 3 Duane, Mr. Frank male 65 0 0 336439 7.75 Q +282 0 3 Olsson, Mr. Nils Johan Goransson male 28 0 0 347464 7.8542 S +283 0 3 de Pelsmaeker, Mr. Alfons male 16 0 0 345778 9.5 S +284 1 3 Dorking, Mr. Edward Arthur male 19 0 0 A/5. 10482 8.05 S +285 0 1 Smith, Mr. Richard William male 0 0 113056 26 A19 S +286 0 3 Stankovic, Mr. Ivan male 33 0 0 349239 8.6625 C +287 1 3 de Mulder, Mr. Theodore male 30 0 0 345774 9.5 S +288 0 3 Naidenoff, Mr. Penko male 22 0 0 349206 7.8958 S +289 1 2 Hosono, Mr. Masabumi male 42 0 0 237798 13 S +290 1 3 Connolly, Miss. Kate female 22 0 0 370373 7.75 Q +291 1 1 "Barber, Miss. Ellen ""Nellie""" female 26 0 0 19877 78.85 S +292 1 1 Bishop, Mrs. Dickinson H (Helen Walton) female 19 1 0 11967 91.0792 B49 C +293 0 2 Levy, Mr. Rene Jacques male 36 0 0 SC/Paris 2163 12.875 D C +294 0 3 Haas, Miss. Aloisia female 24 0 0 349236 8.85 S +295 0 3 Mineff, Mr. Ivan male 24 0 0 349233 7.8958 S +296 0 1 Lewy, Mr. Ervin G male 0 0 PC 17612 27.7208 C +297 0 3 Hanna, Mr. Mansour male 23.5 0 0 2693 7.2292 C +298 0 1 Allison, Miss. Helen Loraine female 2 1 2 113781 151.55 C22 C26 S +299 1 1 Saalfeld, Mr. Adolphe male 0 0 19988 30.5 C106 S +300 1 1 Baxter, Mrs. James (Helene DeLaudeniere Chaput) female 50 0 1 PC 17558 247.5208 B58 B60 C +301 1 3 "Kelly, Miss. Anna Katherine ""Annie Kate""" female 0 0 9234 7.75 Q +302 1 3 McCoy, Mr. Bernard male 2 0 367226 23.25 Q +303 0 3 Johnson, Mr. William Cahoone Jr male 19 0 0 LINE 0 S +304 1 2 Keane, Miss. Nora A female 0 0 226593 12.35 E101 Q +305 0 3 "Williams, Mr. Howard Hugh ""Harry""" male 0 0 A/5 2466 8.05 S +306 1 1 Allison, Master. Hudson Trevor male 0.92 1 2 113781 151.55 C22 C26 S +307 1 1 Fleming, Miss. Margaret female 0 0 17421 110.8833 C +308 1 1 Penasco y Castellana, Mrs. Victor de Satode (Maria Josefa Perez de Soto y Vallejo) female 17 1 0 PC 17758 108.9 C65 C +309 0 2 Abelson, Mr. Samuel male 30 1 0 P/PP 3381 24 C +310 1 1 Francatelli, Miss. Laura Mabel female 30 0 0 PC 17485 56.9292 E36 C +311 1 1 Hays, Miss. Margaret Bechstein female 24 0 0 11767 83.1583 C54 C +312 1 1 Ryerson, Miss. Emily Borie female 18 2 2 PC 17608 262.375 B57 B59 B63 B66 C +313 0 2 Lahtinen, Mrs. William (Anna Sylfven) female 26 1 1 250651 26 S +314 0 3 Hendekovic, Mr. Ignjac male 28 0 0 349243 7.8958 S +315 0 2 Hart, Mr. Benjamin male 43 1 1 F.C.C. 13529 26.25 S +316 1 3 Nilsson, Miss. Helmina Josefina female 26 0 0 347470 7.8542 S +317 1 2 Kantor, Mrs. Sinai (Miriam Sternin) female 24 1 0 244367 26 S +318 0 2 Moraweck, Dr. Ernest male 54 0 0 29011 14 S +319 1 1 Wick, Miss. Mary Natalie female 31 0 2 36928 164.8667 C7 S +320 1 1 Spedden, Mrs. Frederic Oakley (Margaretta Corning Stone) female 40 1 1 16966 134.5 E34 C +321 0 3 Dennis, Mr. Samuel male 22 0 0 A/5 21172 7.25 S +322 0 3 Danoff, Mr. Yoto male 27 0 0 349219 7.8958 S +323 1 2 Slayter, Miss. Hilda Mary female 30 0 0 234818 12.35 Q +324 1 2 Caldwell, Mrs. Albert Francis (Sylvia Mae Harbaugh) female 22 1 1 248738 29 S +325 0 3 Sage, Mr. George John Jr male 8 2 CA. 2343 69.55 S +326 1 1 Young, Miss. Marie Grice female 36 0 0 PC 17760 135.6333 C32 C +327 0 3 Nysveen, Mr. Johan Hansen male 61 0 0 345364 6.2375 S +328 1 2 Ball, Mrs. (Ada E Hall) female 36 0 0 28551 13 D S +329 1 3 Goldsmith, Mrs. Frank John (Emily Alice Brown) female 31 1 1 363291 20.525 S +330 1 1 Hippach, Miss. Jean Gertrude female 16 0 1 111361 57.9792 B18 C +331 1 3 McCoy, Miss. Agnes female 2 0 367226 23.25 Q +332 0 1 Partner, Mr. Austen male 45.5 0 0 113043 28.5 C124 S +333 0 1 Graham, Mr. George Edward male 38 0 1 PC 17582 153.4625 C91 S +334 0 3 Vander Planke, Mr. Leo Edmondus male 16 2 0 345764 18 S +335 1 1 Frauenthal, Mrs. Henry William (Clara Heinsheimer) female 1 0 PC 17611 133.65 S +336 0 3 Denkoff, Mr. Mitto male 0 0 349225 7.8958 S +337 0 1 Pears, Mr. Thomas Clinton male 29 1 0 113776 66.6 C2 S +338 1 1 Burns, Miss. Elizabeth Margaret female 41 0 0 16966 134.5 E40 C +339 1 3 Dahl, Mr. Karl Edwart male 45 0 0 7598 8.05 S +340 0 1 Blackwell, Mr. Stephen Weart male 45 0 0 113784 35.5 T S +341 1 2 Navratil, Master. Edmond Roger male 2 1 1 230080 26 F2 S +342 1 1 Fortune, Miss. Alice Elizabeth female 24 3 2 19950 263 C23 C25 C27 S +343 0 2 Collander, Mr. Erik Gustaf male 28 0 0 248740 13 S +344 0 2 Sedgwick, Mr. Charles Frederick Waddington male 25 0 0 244361 13 S +345 0 2 Fox, Mr. Stanley Hubert male 36 0 0 229236 13 S +346 1 2 "Brown, Miss. Amelia ""Mildred""" female 24 0 0 248733 13 F33 S +347 1 2 Smith, Miss. Marion Elsie female 40 0 0 31418 13 S +348 1 3 Davison, Mrs. Thomas Henry (Mary E Finck) female 1 0 386525 16.1 S +349 1 3 "Coutts, Master. William Loch ""William""" male 3 1 1 C.A. 37671 15.9 S +350 0 3 Dimic, Mr. Jovan male 42 0 0 315088 8.6625 S +351 0 3 Odahl, Mr. Nils Martin male 23 0 0 7267 9.225 S +352 0 1 Williams-Lambert, Mr. Fletcher Fellows male 0 0 113510 35 C128 S +353 0 3 Elias, Mr. Tannous male 15 1 1 2695 7.2292 C +354 0 3 Arnold-Franchi, Mr. Josef male 25 1 0 349237 17.8 S +355 0 3 Yousif, Mr. Wazli male 0 0 2647 7.225 C +356 0 3 Vanden Steen, Mr. Leo Peter male 28 0 0 345783 9.5 S +357 1 1 Bowerman, Miss. Elsie Edith female 22 0 1 113505 55 E33 S +358 0 2 Funk, Miss. Annie Clemmer female 38 0 0 237671 13 S +359 1 3 McGovern, Miss. Mary female 0 0 330931 7.8792 Q +360 1 3 "Mockler, Miss. Helen Mary ""Ellie""" female 0 0 330980 7.8792 Q +361 0 3 Skoog, Mr. Wilhelm male 40 1 4 347088 27.9 S +362 0 2 del Carlo, Mr. Sebastiano male 29 1 0 SC/PARIS 2167 27.7208 C +363 0 3 Barbara, Mrs. (Catherine David) female 45 0 1 2691 14.4542 C +364 0 3 Asim, Mr. Adola male 35 0 0 SOTON/O.Q. 3101310 7.05 S +365 0 3 O'Brien, Mr. Thomas male 1 0 370365 15.5 Q +366 0 3 Adahl, Mr. Mauritz Nils Martin male 30 0 0 C 7076 7.25 S +367 1 1 Warren, Mrs. Frank Manley (Anna Sophia Atkinson) female 60 1 0 110813 75.25 D37 C +368 1 3 Moussa, Mrs. (Mantoura Boulos) female 0 0 2626 7.2292 C +369 1 3 Jermyn, Miss. Annie female 0 0 14313 7.75 Q +370 1 1 Aubart, Mme. Leontine Pauline female 24 0 0 PC 17477 69.3 B35 C +371 1 1 Harder, Mr. George Achilles male 25 1 0 11765 55.4417 E50 C +372 0 3 Wiklund, Mr. Jakob Alfred male 18 1 0 3101267 6.4958 S +373 0 3 Beavan, Mr. William Thomas male 19 0 0 323951 8.05 S +374 0 1 Ringhini, Mr. Sante male 22 0 0 PC 17760 135.6333 C +375 0 3 Palsson, Miss. Stina Viola female 3 3 1 349909 21.075 S +376 1 1 Meyer, Mrs. Edgar Joseph (Leila Saks) female 1 0 PC 17604 82.1708 C +377 1 3 Landergren, Miss. Aurora Adelia female 22 0 0 C 7077 7.25 S +378 0 1 Widener, Mr. Harry Elkins male 27 0 2 113503 211.5 C82 C +379 0 3 Betros, Mr. Tannous male 20 0 0 2648 4.0125 C +380 0 3 Gustafsson, Mr. Karl Gideon male 19 0 0 347069 7.775 S +381 1 1 Bidois, Miss. Rosalie female 42 0 0 PC 17757 227.525 C +382 1 3 "Nakid, Miss. Maria (""Mary"")" female 1 0 2 2653 15.7417 C +383 0 3 Tikkanen, Mr. Juho male 32 0 0 STON/O 2. 3101293 7.925 S +384 1 1 Holverson, Mrs. Alexander Oskar (Mary Aline Towner) female 35 1 0 113789 52 S +385 0 3 Plotcharsky, Mr. Vasil male 0 0 349227 7.8958 S +386 0 2 Davies, Mr. Charles Henry male 18 0 0 S.O.C. 14879 73.5 S +387 0 3 Goodwin, Master. Sidney Leonard male 1 5 2 CA 2144 46.9 S +388 1 2 Buss, Miss. Kate female 36 0 0 27849 13 S +389 0 3 Sadlier, Mr. Matthew male 0 0 367655 7.7292 Q +390 1 2 Lehmann, Miss. Bertha female 17 0 0 SC 1748 12 C +391 1 1 Carter, Mr. William Ernest male 36 1 2 113760 120 B96 B98 S +392 1 3 Jansson, Mr. Carl Olof male 21 0 0 350034 7.7958 S +393 0 3 Gustafsson, Mr. Johan Birger male 28 2 0 3101277 7.925 S +394 1 1 Newell, Miss. Marjorie female 23 1 0 35273 113.275 D36 C +395 1 3 Sandstrom, Mrs. Hjalmar (Agnes Charlotta Bengtsson) female 24 0 2 PP 9549 16.7 G6 S +396 0 3 Johansson, Mr. Erik male 22 0 0 350052 7.7958 S +397 0 3 Olsson, Miss. Elina female 31 0 0 350407 7.8542 S +398 0 2 McKane, Mr. Peter David male 46 0 0 28403 26 S +399 0 2 Pain, Dr. Alfred male 23 0 0 244278 10.5 S +400 1 2 Trout, Mrs. William H (Jessie L) female 28 0 0 240929 12.65 S +401 1 3 Niskanen, Mr. Juha male 39 0 0 STON/O 2. 3101289 7.925 S +402 0 3 Adams, Mr. John male 26 0 0 341826 8.05 S +403 0 3 Jussila, Miss. Mari Aina female 21 1 0 4137 9.825 S +404 0 3 Hakkarainen, Mr. Pekka Pietari male 28 1 0 STON/O2. 3101279 15.85 S +405 0 3 Oreskovic, Miss. Marija female 20 0 0 315096 8.6625 S +406 0 2 Gale, Mr. Shadrach male 34 1 0 28664 21 S +407 0 3 Widegren, Mr. Carl/Charles Peter male 51 0 0 347064 7.75 S +408 1 2 Richards, Master. William Rowe male 3 1 1 29106 18.75 S +409 0 3 Birkeland, Mr. Hans Martin Monsen male 21 0 0 312992 7.775 S +410 0 3 Lefebre, Miss. Ida female 3 1 4133 25.4667 S +411 0 3 Sdycoff, Mr. Todor male 0 0 349222 7.8958 S +412 0 3 Hart, Mr. Henry male 0 0 394140 6.8583 Q +413 1 1 Minahan, Miss. Daisy E female 33 1 0 19928 90 C78 Q +414 0 2 Cunningham, Mr. Alfred Fleming male 0 0 239853 0 S +415 1 3 Sundman, Mr. Johan Julian male 44 0 0 STON/O 2. 3101269 7.925 S +416 0 3 Meek, Mrs. Thomas (Annie Louise Rowley) female 0 0 343095 8.05 S +417 1 2 Drew, Mrs. James Vivian (Lulu Thorne Christian) female 34 1 1 28220 32.5 S +418 1 2 Silven, Miss. Lyyli Karoliina female 18 0 2 250652 13 S +419 0 2 Matthews, Mr. William John male 30 0 0 28228 13 S +420 0 3 Van Impe, Miss. Catharina female 10 0 2 345773 24.15 S +421 0 3 Gheorgheff, Mr. Stanio male 0 0 349254 7.8958 C +422 0 3 Charters, Mr. David male 21 0 0 A/5. 13032 7.7333 Q +423 0 3 Zimmerman, Mr. Leo male 29 0 0 315082 7.875 S +424 0 3 Danbom, Mrs. Ernst Gilbert (Anna Sigrid Maria Brogren) female 28 1 1 347080 14.4 S +425 0 3 Rosblom, Mr. Viktor Richard male 18 1 1 370129 20.2125 S +426 0 3 Wiseman, Mr. Phillippe male 0 0 A/4. 34244 7.25 S +427 1 2 Clarke, Mrs. Charles V (Ada Maria Winfield) female 28 1 0 2003 26 S +428 1 2 "Phillips, Miss. Kate Florence (""Mrs Kate Louise Phillips Marshall"")" female 19 0 0 250655 26 S +429 0 3 Flynn, Mr. James male 0 0 364851 7.75 Q +430 1 3 Pickard, Mr. Berk (Berk Trembisky) male 32 0 0 SOTON/O.Q. 392078 8.05 E10 S +431 1 1 Bjornstrom-Steffansson, Mr. Mauritz Hakan male 28 0 0 110564 26.55 C52 S +432 1 3 Thorneycroft, Mrs. Percival (Florence Kate White) female 1 0 376564 16.1 S +433 1 2 Louch, Mrs. Charles Alexander (Alice Adelaide Slow) female 42 1 0 SC/AH 3085 26 S +434 0 3 Kallio, Mr. Nikolai Erland male 17 0 0 STON/O 2. 3101274 7.125 S +435 0 1 Silvey, Mr. William Baird male 50 1 0 13507 55.9 E44 S +436 1 1 Carter, Miss. Lucile Polk female 14 1 2 113760 120 B96 B98 S +437 0 3 "Ford, Miss. Doolina Margaret ""Daisy""" female 21 2 2 W./C. 6608 34.375 S +438 1 2 Richards, Mrs. Sidney (Emily Hocking) female 24 2 3 29106 18.75 S +439 0 1 Fortune, Mr. Mark male 64 1 4 19950 263 C23 C25 C27 S +440 0 2 Kvillner, Mr. Johan Henrik Johannesson male 31 0 0 C.A. 18723 10.5 S +441 1 2 Hart, Mrs. Benjamin (Esther Ada Bloomfield) female 45 1 1 F.C.C. 13529 26.25 S +442 0 3 Hampe, Mr. Leon male 20 0 0 345769 9.5 S +443 0 3 Petterson, Mr. Johan Emil male 25 1 0 347076 7.775 S +444 1 2 Reynaldo, Ms. Encarnacion female 28 0 0 230434 13 S +445 1 3 Johannesen-Bratthammer, Mr. Bernt male 0 0 65306 8.1125 S +446 1 1 Dodge, Master. Washington male 4 0 2 33638 81.8583 A34 S +447 1 2 Mellinger, Miss. Madeleine Violet female 13 0 1 250644 19.5 S +448 1 1 Seward, Mr. Frederic Kimber male 34 0 0 113794 26.55 S +449 1 3 Baclini, Miss. Marie Catherine female 5 2 1 2666 19.2583 C +450 1 1 Peuchen, Major. Arthur Godfrey male 52 0 0 113786 30.5 C104 S +451 0 2 West, Mr. Edwy Arthur male 36 1 2 C.A. 34651 27.75 S +452 0 3 Hagland, Mr. Ingvald Olai Olsen male 1 0 65303 19.9667 S +453 0 1 Foreman, Mr. Benjamin Laventall male 30 0 0 113051 27.75 C111 C +454 1 1 Goldenberg, Mr. Samuel L male 49 1 0 17453 89.1042 C92 C +455 0 3 Peduzzi, Mr. Joseph male 0 0 A/5 2817 8.05 S +456 1 3 Jalsevac, Mr. Ivan male 29 0 0 349240 7.8958 C +457 0 1 Millet, Mr. Francis Davis male 65 0 0 13509 26.55 E38 S +458 1 1 Kenyon, Mrs. Frederick R (Marion) female 1 0 17464 51.8625 D21 S +459 1 2 Toomey, Miss. Ellen female 50 0 0 F.C.C. 13531 10.5 S +460 0 3 O'Connor, Mr. Maurice male 0 0 371060 7.75 Q +461 1 1 Anderson, Mr. Harry male 48 0 0 19952 26.55 E12 S +462 0 3 Morley, Mr. William male 34 0 0 364506 8.05 S +463 0 1 Gee, Mr. Arthur H male 47 0 0 111320 38.5 E63 S +464 0 2 Milling, Mr. Jacob Christian male 48 0 0 234360 13 S +465 0 3 Maisner, Mr. Simon male 0 0 A/S 2816 8.05 S +466 0 3 Goncalves, Mr. Manuel Estanslas male 38 0 0 SOTON/O.Q. 3101306 7.05 S +467 0 2 Campbell, Mr. William male 0 0 239853 0 S +468 0 1 Smart, Mr. John Montgomery male 56 0 0 113792 26.55 S +469 0 3 Scanlan, Mr. James male 0 0 36209 7.725 Q +470 1 3 Baclini, Miss. Helene Barbara female 0.75 2 1 2666 19.2583 C +471 0 3 Keefe, Mr. Arthur male 0 0 323592 7.25 S +472 0 3 Cacic, Mr. Luka male 38 0 0 315089 8.6625 S +473 1 2 West, Mrs. Edwy Arthur (Ada Mary Worth) female 33 1 2 C.A. 34651 27.75 S +474 1 2 Jerwan, Mrs. Amin S (Marie Marthe Thuillard) female 23 0 0 SC/AH Basle 541 13.7917 D C +475 0 3 Strandberg, Miss. Ida Sofia female 22 0 0 7553 9.8375 S +476 0 1 Clifford, Mr. George Quincy male 0 0 110465 52 A14 S +477 0 2 Renouf, Mr. Peter Henry male 34 1 0 31027 21 S +478 0 3 Braund, Mr. Lewis Richard male 29 1 0 3460 7.0458 S +479 0 3 Karlsson, Mr. Nils August male 22 0 0 350060 7.5208 S +480 1 3 Hirvonen, Miss. Hildur E female 2 0 1 3101298 12.2875 S +481 0 3 Goodwin, Master. Harold Victor male 9 5 2 CA 2144 46.9 S +482 0 2 "Frost, Mr. Anthony Wood ""Archie""" male 0 0 239854 0 S +483 0 3 Rouse, Mr. Richard Henry male 50 0 0 A/5 3594 8.05 S +484 1 3 Turkula, Mrs. (Hedwig) female 63 0 0 4134 9.5875 S +485 1 1 Bishop, Mr. Dickinson H male 25 1 0 11967 91.0792 B49 C +486 0 3 Lefebre, Miss. Jeannie female 3 1 4133 25.4667 S +487 1 1 Hoyt, Mrs. Frederick Maxfield (Jane Anne Forby) female 35 1 0 19943 90 C93 S +488 0 1 Kent, Mr. Edward Austin male 58 0 0 11771 29.7 B37 C +489 0 3 Somerton, Mr. Francis William male 30 0 0 A.5. 18509 8.05 S +490 1 3 "Coutts, Master. Eden Leslie ""Neville""" male 9 1 1 C.A. 37671 15.9 S +491 0 3 Hagland, Mr. Konrad Mathias Reiersen male 1 0 65304 19.9667 S +492 0 3 Windelov, Mr. Einar male 21 0 0 SOTON/OQ 3101317 7.25 S +493 0 1 Molson, Mr. Harry Markland male 55 0 0 113787 30.5 C30 S +494 0 1 Artagaveytia, Mr. Ramon male 71 0 0 PC 17609 49.5042 C +495 0 3 Stanley, Mr. Edward Roland male 21 0 0 A/4 45380 8.05 S +496 0 3 Yousseff, Mr. Gerious male 0 0 2627 14.4583 C +497 1 1 Eustis, Miss. Elizabeth Mussey female 54 1 0 36947 78.2667 D20 C +498 0 3 Shellard, Mr. Frederick William male 0 0 C.A. 6212 15.1 S +499 0 1 Allison, Mrs. Hudson J C (Bessie Waldo Daniels) female 25 1 2 113781 151.55 C22 C26 S +500 0 3 Svensson, Mr. Olof male 24 0 0 350035 7.7958 S +501 0 3 Calic, Mr. Petar male 17 0 0 315086 8.6625 S +502 0 3 Canavan, Miss. Mary female 21 0 0 364846 7.75 Q +503 0 3 O'Sullivan, Miss. Bridget Mary female 0 0 330909 7.6292 Q +504 0 3 Laitinen, Miss. Kristina Sofia female 37 0 0 4135 9.5875 S +505 1 1 Maioni, Miss. Roberta female 16 0 0 110152 86.5 B79 S +506 0 1 Penasco y Castellana, Mr. Victor de Satode male 18 1 0 PC 17758 108.9 C65 C +507 1 2 Quick, Mrs. Frederick Charles (Jane Richards) female 33 0 2 26360 26 S +508 1 1 "Bradley, Mr. George (""George Arthur Brayton"")" male 0 0 111427 26.55 S +509 0 3 Olsen, Mr. Henry Margido male 28 0 0 C 4001 22.525 S +510 1 3 Lang, Mr. Fang male 26 0 0 1601 56.4958 S +511 1 3 Daly, Mr. Eugene Patrick male 29 0 0 382651 7.75 Q +512 0 3 Webber, Mr. James male 0 0 SOTON/OQ 3101316 8.05 S +513 1 1 McGough, Mr. James Robert male 36 0 0 PC 17473 26.2875 E25 S +514 1 1 Rothschild, Mrs. Martin (Elizabeth L. Barrett) female 54 1 0 PC 17603 59.4 C +515 0 3 Coleff, Mr. Satio male 24 0 0 349209 7.4958 S +516 0 1 Walker, Mr. William Anderson male 47 0 0 36967 34.0208 D46 S +517 1 2 Lemore, Mrs. (Amelia Milley) female 34 0 0 C.A. 34260 10.5 F33 S +518 0 3 Ryan, Mr. Patrick male 0 0 371110 24.15 Q +519 1 2 "Angle, Mrs. William A (Florence ""Mary"" Agnes Hughes)" female 36 1 0 226875 26 S +520 0 3 Pavlovic, Mr. Stefo male 32 0 0 349242 7.8958 S +521 1 1 Perreault, Miss. Anne female 30 0 0 12749 93.5 B73 S +522 0 3 Vovk, Mr. Janko male 22 0 0 349252 7.8958 S +523 0 3 Lahoud, Mr. Sarkis male 0 0 2624 7.225 C +524 1 1 Hippach, Mrs. Louis Albert (Ida Sophia Fischer) female 44 0 1 111361 57.9792 B18 C +525 0 3 Kassem, Mr. Fared male 0 0 2700 7.2292 C +526 0 3 Farrell, Mr. James male 40.5 0 0 367232 7.75 Q +527 1 2 Ridsdale, Miss. Lucy female 50 0 0 W./C. 14258 10.5 S +528 0 1 Farthing, Mr. John male 0 0 PC 17483 221.7792 C95 S +529 0 3 Salonen, Mr. Johan Werner male 39 0 0 3101296 7.925 S +530 0 2 Hocking, Mr. Richard George male 23 2 1 29104 11.5 S +531 1 2 Quick, Miss. Phyllis May female 2 1 1 26360 26 S +532 0 3 Toufik, Mr. Nakli male 0 0 2641 7.2292 C +533 0 3 Elias, Mr. Joseph Jr male 17 1 1 2690 7.2292 C +534 1 3 Peter, Mrs. Catherine (Catherine Rizk) female 0 2 2668 22.3583 C +535 0 3 Cacic, Miss. Marija female 30 0 0 315084 8.6625 S +536 1 2 Hart, Miss. Eva Miriam female 7 0 2 F.C.C. 13529 26.25 S +537 0 1 Butt, Major. Archibald Willingham male 45 0 0 113050 26.55 B38 S +538 1 1 LeRoy, Miss. Bertha female 30 0 0 PC 17761 106.425 C +539 0 3 Risien, Mr. Samuel Beard male 0 0 364498 14.5 S +540 1 1 Frolicher, Miss. Hedwig Margaritha female 22 0 2 13568 49.5 B39 C +541 1 1 Crosby, Miss. Harriet R female 36 0 2 WE/P 5735 71 B22 S +542 0 3 Andersson, Miss. Ingeborg Constanzia female 9 4 2 347082 31.275 S +543 0 3 Andersson, Miss. Sigrid Elisabeth female 11 4 2 347082 31.275 S +544 1 2 Beane, Mr. Edward male 32 1 0 2908 26 S +545 0 1 Douglas, Mr. Walter Donald male 50 1 0 PC 17761 106.425 C86 C +546 0 1 Nicholson, Mr. Arthur Ernest male 64 0 0 693 26 S +547 1 2 Beane, Mrs. Edward (Ethel Clarke) female 19 1 0 2908 26 S +548 1 2 Padro y Manent, Mr. Julian male 0 0 SC/PARIS 2146 13.8625 C +549 0 3 Goldsmith, Mr. Frank John male 33 1 1 363291 20.525 S +550 1 2 Davies, Master. John Morgan Jr male 8 1 1 C.A. 33112 36.75 S +551 1 1 Thayer, Mr. John Borland Jr male 17 0 2 17421 110.8833 C70 C +552 0 2 Sharp, Mr. Percival James R male 27 0 0 244358 26 S +553 0 3 O'Brien, Mr. Timothy male 0 0 330979 7.8292 Q +554 1 3 "Leeni, Mr. Fahim (""Philip Zenni"")" male 22 0 0 2620 7.225 C +555 1 3 Ohman, Miss. Velin female 22 0 0 347085 7.775 S +556 0 1 Wright, Mr. George male 62 0 0 113807 26.55 S +557 1 1 "Duff Gordon, Lady. (Lucille Christiana Sutherland) (""Mrs Morgan"")" female 48 1 0 11755 39.6 A16 C +558 0 1 Robbins, Mr. Victor male 0 0 PC 17757 227.525 C +559 1 1 Taussig, Mrs. Emil (Tillie Mandelbaum) female 39 1 1 110413 79.65 E67 S +560 1 3 de Messemaeker, Mrs. Guillaume Joseph (Emma) female 36 1 0 345572 17.4 S +561 0 3 Morrow, Mr. Thomas Rowan male 0 0 372622 7.75 Q +562 0 3 Sivic, Mr. Husein male 40 0 0 349251 7.8958 S +563 0 2 Norman, Mr. Robert Douglas male 28 0 0 218629 13.5 S +564 0 3 Simmons, Mr. John male 0 0 SOTON/OQ 392082 8.05 S +565 0 3 Meanwell, Miss. (Marion Ogden) female 0 0 SOTON/O.Q. 392087 8.05 S +566 0 3 Davies, Mr. Alfred J male 24 2 0 A/4 48871 24.15 S +567 0 3 Stoytcheff, Mr. Ilia male 19 0 0 349205 7.8958 S +568 0 3 Palsson, Mrs. Nils (Alma Cornelia Berglund) female 29 0 4 349909 21.075 S +569 0 3 Doharr, Mr. Tannous male 0 0 2686 7.2292 C +570 1 3 Jonsson, Mr. Carl male 32 0 0 350417 7.8542 S +571 1 2 Harris, Mr. George male 62 0 0 S.W./PP 752 10.5 S +572 1 1 Appleton, Mrs. Edward Dale (Charlotte Lamson) female 53 2 0 11769 51.4792 C101 S +573 1 1 "Flynn, Mr. John Irwin (""Irving"")" male 36 0 0 PC 17474 26.3875 E25 S +574 1 3 Kelly, Miss. Mary female 0 0 14312 7.75 Q +575 0 3 Rush, Mr. Alfred George John male 16 0 0 A/4. 20589 8.05 S +576 0 3 Patchett, Mr. George male 19 0 0 358585 14.5 S +577 1 2 Garside, Miss. Ethel female 34 0 0 243880 13 S +578 1 1 Silvey, Mrs. William Baird (Alice Munger) female 39 1 0 13507 55.9 E44 S +579 0 3 Caram, Mrs. Joseph (Maria Elias) female 1 0 2689 14.4583 C +580 1 3 Jussila, Mr. Eiriik male 32 0 0 STON/O 2. 3101286 7.925 S +581 1 2 Christy, Miss. Julie Rachel female 25 1 1 237789 30 S +582 1 1 Thayer, Mrs. John Borland (Marian Longstreth Morris) female 39 1 1 17421 110.8833 C68 C +583 0 2 Downton, Mr. William James male 54 0 0 28403 26 S +584 0 1 Ross, Mr. John Hugo male 36 0 0 13049 40.125 A10 C +585 0 3 Paulner, Mr. Uscher male 0 0 3411 8.7125 C +586 1 1 Taussig, Miss. Ruth female 18 0 2 110413 79.65 E68 S +587 0 2 Jarvis, Mr. John Denzil male 47 0 0 237565 15 S +588 1 1 Frolicher-Stehli, Mr. Maxmillian male 60 1 1 13567 79.2 B41 C +589 0 3 Gilinski, Mr. Eliezer male 22 0 0 14973 8.05 S +590 0 3 Murdlin, Mr. Joseph male 0 0 A./5. 3235 8.05 S +591 0 3 Rintamaki, Mr. Matti male 35 0 0 STON/O 2. 3101273 7.125 S +592 1 1 Stephenson, Mrs. Walter Bertram (Martha Eustis) female 52 1 0 36947 78.2667 D20 C +593 0 3 Elsbury, Mr. William James male 47 0 0 A/5 3902 7.25 S +594 0 3 Bourke, Miss. Mary female 0 2 364848 7.75 Q +595 0 2 Chapman, Mr. John Henry male 37 1 0 SC/AH 29037 26 S +596 0 3 Van Impe, Mr. Jean Baptiste male 36 1 1 345773 24.15 S +597 1 2 Leitch, Miss. Jessie Wills female 0 0 248727 33 S +598 0 3 Johnson, Mr. Alfred male 49 0 0 LINE 0 S +599 0 3 Boulos, Mr. Hanna male 0 0 2664 7.225 C +600 1 1 "Duff Gordon, Sir. Cosmo Edmund (""Mr Morgan"")" male 49 1 0 PC 17485 56.9292 A20 C +601 1 2 Jacobsohn, Mrs. Sidney Samuel (Amy Frances Christy) female 24 2 1 243847 27 S +602 0 3 Slabenoff, Mr. Petco male 0 0 349214 7.8958 S +603 0 1 Harrington, Mr. Charles H male 0 0 113796 42.4 S +604 0 3 Torber, Mr. Ernst William male 44 0 0 364511 8.05 S +605 1 1 "Homer, Mr. Harry (""Mr E Haven"")" male 35 0 0 111426 26.55 C +606 0 3 Lindell, Mr. Edvard Bengtsson male 36 1 0 349910 15.55 S +607 0 3 Karaic, Mr. Milan male 30 0 0 349246 7.8958 S +608 1 1 Daniel, Mr. Robert Williams male 27 0 0 113804 30.5 S +609 1 2 Laroche, Mrs. Joseph (Juliette Marie Louise Lafargue) female 22 1 2 SC/Paris 2123 41.5792 C +610 1 1 Shutes, Miss. Elizabeth W female 40 0 0 PC 17582 153.4625 C125 S +611 0 3 Andersson, Mrs. Anders Johan (Alfrida Konstantia Brogren) female 39 1 5 347082 31.275 S +612 0 3 Jardin, Mr. Jose Neto male 0 0 SOTON/O.Q. 3101305 7.05 S +613 1 3 Murphy, Miss. Margaret Jane female 1 0 367230 15.5 Q +614 0 3 Horgan, Mr. John male 0 0 370377 7.75 Q +615 0 3 Brocklebank, Mr. William Alfred male 35 0 0 364512 8.05 S +616 1 2 Herman, Miss. Alice female 24 1 2 220845 65 S +617 0 3 Danbom, Mr. Ernst Gilbert male 34 1 1 347080 14.4 S +618 0 3 Lobb, Mrs. William Arthur (Cordelia K Stanlick) female 26 1 0 A/5. 3336 16.1 S +619 1 2 Becker, Miss. Marion Louise female 4 2 1 230136 39 F4 S +620 0 2 Gavey, Mr. Lawrence male 26 0 0 31028 10.5 S +621 0 3 Yasbeck, Mr. Antoni male 27 1 0 2659 14.4542 C +622 1 1 Kimball, Mr. Edwin Nelson Jr male 42 1 0 11753 52.5542 D19 S +623 1 3 Nakid, Mr. Sahid male 20 1 1 2653 15.7417 C +624 0 3 Hansen, Mr. Henry Damsgaard male 21 0 0 350029 7.8542 S +625 0 3 "Bowen, Mr. David John ""Dai""" male 21 0 0 54636 16.1 S +626 0 1 Sutton, Mr. Frederick male 61 0 0 36963 32.3208 D50 S +627 0 2 Kirkland, Rev. Charles Leonard male 57 0 0 219533 12.35 Q +628 1 1 Longley, Miss. Gretchen Fiske female 21 0 0 13502 77.9583 D9 S +629 0 3 Bostandyeff, Mr. Guentcho male 26 0 0 349224 7.8958 S +630 0 3 O'Connell, Mr. Patrick D male 0 0 334912 7.7333 Q +631 1 1 Barkworth, Mr. Algernon Henry Wilson male 80 0 0 27042 30 A23 S +632 0 3 Lundahl, Mr. Johan Svensson male 51 0 0 347743 7.0542 S +633 1 1 Stahelin-Maeglin, Dr. Max male 32 0 0 13214 30.5 B50 C +634 0 1 Parr, Mr. William Henry Marsh male 0 0 112052 0 S +635 0 3 Skoog, Miss. Mabel female 9 3 2 347088 27.9 S +636 1 2 Davis, Miss. Mary female 28 0 0 237668 13 S +637 0 3 Leinonen, Mr. Antti Gustaf male 32 0 0 STON/O 2. 3101292 7.925 S +638 0 2 Collyer, Mr. Harvey male 31 1 1 C.A. 31921 26.25 S +639 0 3 Panula, Mrs. Juha (Maria Emilia Ojala) female 41 0 5 3101295 39.6875 S +640 0 3 Thorneycroft, Mr. Percival male 1 0 376564 16.1 S +641 0 3 Jensen, Mr. Hans Peder male 20 0 0 350050 7.8542 S +642 1 1 Sagesser, Mlle. Emma female 24 0 0 PC 17477 69.3 B35 C +643 0 3 Skoog, Miss. Margit Elizabeth female 2 3 2 347088 27.9 S +644 1 3 Foo, Mr. Choong male 0 0 1601 56.4958 S +645 1 3 Baclini, Miss. Eugenie female 0.75 2 1 2666 19.2583 C +646 1 1 Harper, Mr. Henry Sleeper male 48 1 0 PC 17572 76.7292 D33 C +647 0 3 Cor, Mr. Liudevit male 19 0 0 349231 7.8958 S +648 1 1 Simonius-Blumer, Col. Oberst Alfons male 56 0 0 13213 35.5 A26 C +649 0 3 Willey, Mr. Edward male 0 0 S.O./P.P. 751 7.55 S +650 1 3 Stanley, Miss. Amy Zillah Elsie female 23 0 0 CA. 2314 7.55 S +651 0 3 Mitkoff, Mr. Mito male 0 0 349221 7.8958 S +652 1 2 Doling, Miss. Elsie female 18 0 1 231919 23 S +653 0 3 Kalvik, Mr. Johannes Halvorsen male 21 0 0 8475 8.4333 S +654 1 3 "O'Leary, Miss. Hanora ""Norah""" female 0 0 330919 7.8292 Q +655 0 3 "Hegarty, Miss. Hanora ""Nora""" female 18 0 0 365226 6.75 Q +656 0 2 Hickman, Mr. Leonard Mark male 24 2 0 S.O.C. 14879 73.5 S +657 0 3 Radeff, Mr. Alexander male 0 0 349223 7.8958 S +658 0 3 Bourke, Mrs. John (Catherine) female 32 1 1 364849 15.5 Q +659 0 2 Eitemiller, Mr. George Floyd male 23 0 0 29751 13 S +660 0 1 Newell, Mr. Arthur Webster male 58 0 2 35273 113.275 D48 C +661 1 1 Frauenthal, Dr. Henry William male 50 2 0 PC 17611 133.65 S +662 0 3 Badt, Mr. Mohamed male 40 0 0 2623 7.225 C +663 0 1 Colley, Mr. Edward Pomeroy male 47 0 0 5727 25.5875 E58 S +664 0 3 Coleff, Mr. Peju male 36 0 0 349210 7.4958 S +665 1 3 Lindqvist, Mr. Eino William male 20 1 0 STON/O 2. 3101285 7.925 S +666 0 2 Hickman, Mr. Lewis male 32 2 0 S.O.C. 14879 73.5 S +667 0 2 Butler, Mr. Reginald Fenton male 25 0 0 234686 13 S +668 0 3 Rommetvedt, Mr. Knud Paust male 0 0 312993 7.775 S +669 0 3 Cook, Mr. Jacob male 43 0 0 A/5 3536 8.05 S +670 1 1 Taylor, Mrs. Elmer Zebley (Juliet Cummins Wright) female 1 0 19996 52 C126 S +671 1 2 Brown, Mrs. Thomas William Solomon (Elizabeth Catherine Ford) female 40 1 1 29750 39 S +672 0 1 Davidson, Mr. Thornton male 31 1 0 F.C. 12750 52 B71 S +673 0 2 Mitchell, Mr. Henry Michael male 70 0 0 C.A. 24580 10.5 S +674 1 2 Wilhelms, Mr. Charles male 31 0 0 244270 13 S +675 0 2 Watson, Mr. Ennis Hastings male 0 0 239856 0 S +676 0 3 Edvardsson, Mr. Gustaf Hjalmar male 18 0 0 349912 7.775 S +677 0 3 Sawyer, Mr. Frederick Charles male 24.5 0 0 342826 8.05 S +678 1 3 Turja, Miss. Anna Sofia female 18 0 0 4138 9.8417 S +679 0 3 Goodwin, Mrs. Frederick (Augusta Tyler) female 43 1 6 CA 2144 46.9 S +680 1 1 Cardeza, Mr. Thomas Drake Martinez male 36 0 1 PC 17755 512.3292 B51 B53 B55 C +681 0 3 Peters, Miss. Katie female 0 0 330935 8.1375 Q +682 1 1 Hassab, Mr. Hammad male 27 0 0 PC 17572 76.7292 D49 C +683 0 3 Olsvigen, Mr. Thor Anderson male 20 0 0 6563 9.225 S +684 0 3 Goodwin, Mr. Charles Edward male 14 5 2 CA 2144 46.9 S +685 0 2 Brown, Mr. Thomas William Solomon male 60 1 1 29750 39 S +686 0 2 Laroche, Mr. Joseph Philippe Lemercier male 25 1 2 SC/Paris 2123 41.5792 C +687 0 3 Panula, Mr. Jaako Arnold male 14 4 1 3101295 39.6875 S +688 0 3 Dakic, Mr. Branko male 19 0 0 349228 10.1708 S +689 0 3 Fischer, Mr. Eberhard Thelander male 18 0 0 350036 7.7958 S +690 1 1 Madill, Miss. Georgette Alexandra female 15 0 1 24160 211.3375 B5 S +691 1 1 Dick, Mr. Albert Adrian male 31 1 0 17474 57 B20 S +692 1 3 Karun, Miss. Manca female 4 0 1 349256 13.4167 C +693 1 3 Lam, Mr. Ali male 0 0 1601 56.4958 S +694 0 3 Saad, Mr. Khalil male 25 0 0 2672 7.225 C +695 0 1 Weir, Col. John male 60 0 0 113800 26.55 S +696 0 2 Chapman, Mr. Charles Henry male 52 0 0 248731 13.5 S +697 0 3 Kelly, Mr. James male 44 0 0 363592 8.05 S +698 1 3 "Mullens, Miss. Katherine ""Katie""" female 0 0 35852 7.7333 Q +699 0 1 Thayer, Mr. John Borland male 49 1 1 17421 110.8833 C68 C +700 0 3 Humblen, Mr. Adolf Mathias Nicolai Olsen male 42 0 0 348121 7.65 F G63 S +701 1 1 Astor, Mrs. John Jacob (Madeleine Talmadge Force) female 18 1 0 PC 17757 227.525 C62 C64 C +702 1 1 Silverthorne, Mr. Spencer Victor male 35 0 0 PC 17475 26.2875 E24 S +703 0 3 Barbara, Miss. Saiide female 18 0 1 2691 14.4542 C +704 0 3 Gallagher, Mr. Martin male 25 0 0 36864 7.7417 Q +705 0 3 Hansen, Mr. Henrik Juul male 26 1 0 350025 7.8542 S +706 0 2 "Morley, Mr. Henry Samuel (""Mr Henry Marshall"")" male 39 0 0 250655 26 S +707 1 2 "Kelly, Mrs. Florence ""Fannie""" female 45 0 0 223596 13.5 S +708 1 1 Calderhead, Mr. Edward Pennington male 42 0 0 PC 17476 26.2875 E24 S +709 1 1 Cleaver, Miss. Alice female 22 0 0 113781 151.55 S +710 1 3 "Moubarek, Master. Halim Gonios (""William George"")" male 1 1 2661 15.2458 C +711 1 1 "Mayne, Mlle. Berthe Antonine (""Mrs de Villiers"")" female 24 0 0 PC 17482 49.5042 C90 C +712 0 1 Klaber, Mr. Herman male 0 0 113028 26.55 C124 S +713 1 1 Taylor, Mr. Elmer Zebley male 48 1 0 19996 52 C126 S +714 0 3 Larsson, Mr. August Viktor male 29 0 0 7545 9.4833 S +715 0 2 Greenberg, Mr. Samuel male 52 0 0 250647 13 S +716 0 3 Soholt, Mr. Peter Andreas Lauritz Andersen male 19 0 0 348124 7.65 F G73 S +717 1 1 Endres, Miss. Caroline Louise female 38 0 0 PC 17757 227.525 C45 C +718 1 2 "Troutt, Miss. Edwina Celia ""Winnie""" female 27 0 0 34218 10.5 E101 S +719 0 3 McEvoy, Mr. Michael male 0 0 36568 15.5 Q +720 0 3 Johnson, Mr. Malkolm Joackim male 33 0 0 347062 7.775 S +721 1 2 "Harper, Miss. Annie Jessie ""Nina""" female 6 0 1 248727 33 S +722 0 3 Jensen, Mr. Svend Lauritz male 17 1 0 350048 7.0542 S +723 0 2 Gillespie, Mr. William Henry male 34 0 0 12233 13 S +724 0 2 Hodges, Mr. Henry Price male 50 0 0 250643 13 S +725 1 1 Chambers, Mr. Norman Campbell male 27 1 0 113806 53.1 E8 S +726 0 3 Oreskovic, Mr. Luka male 20 0 0 315094 8.6625 S +727 1 2 Renouf, Mrs. Peter Henry (Lillian Jefferys) female 30 3 0 31027 21 S +728 1 3 Mannion, Miss. Margareth female 0 0 36866 7.7375 Q +729 0 2 Bryhl, Mr. Kurt Arnold Gottfrid male 25 1 0 236853 26 S +730 0 3 Ilmakangas, Miss. Pieta Sofia female 25 1 0 STON/O2. 3101271 7.925 S +731 1 1 Allen, Miss. Elisabeth Walton female 29 0 0 24160 211.3375 B5 S +732 0 3 Hassan, Mr. Houssein G N male 11 0 0 2699 18.7875 C +733 0 2 Knight, Mr. Robert J male 0 0 239855 0 S +734 0 2 Berriman, Mr. William John male 23 0 0 28425 13 S +735 0 2 Troupiansky, Mr. Moses Aaron male 23 0 0 233639 13 S +736 0 3 Williams, Mr. Leslie male 28.5 0 0 54636 16.1 S +737 0 3 Ford, Mrs. Edward (Margaret Ann Watson) female 48 1 3 W./C. 6608 34.375 S +738 1 1 Lesurer, Mr. Gustave J male 35 0 0 PC 17755 512.3292 B101 C +739 0 3 Ivanoff, Mr. Kanio male 0 0 349201 7.8958 S +740 0 3 Nankoff, Mr. Minko male 0 0 349218 7.8958 S +741 1 1 Hawksford, Mr. Walter James male 0 0 16988 30 D45 S +742 0 1 Cavendish, Mr. Tyrell William male 36 1 0 19877 78.85 C46 S +743 1 1 "Ryerson, Miss. Susan Parker ""Suzette""" female 21 2 2 PC 17608 262.375 B57 B59 B63 B66 C +744 0 3 McNamee, Mr. Neal male 24 1 0 376566 16.1 S +745 1 3 Stranden, Mr. Juho male 31 0 0 STON/O 2. 3101288 7.925 S +746 0 1 Crosby, Capt. Edward Gifford male 70 1 1 WE/P 5735 71 B22 S +747 0 3 Abbott, Mr. Rossmore Edward male 16 1 1 C.A. 2673 20.25 S +748 1 2 Sinkkonen, Miss. Anna female 30 0 0 250648 13 S +749 0 1 Marvin, Mr. Daniel Warner male 19 1 0 113773 53.1 D30 S +750 0 3 Connaghton, Mr. Michael male 31 0 0 335097 7.75 Q +751 1 2 Wells, Miss. Joan female 4 1 1 29103 23 S +752 1 3 Moor, Master. Meier male 6 0 1 392096 12.475 E121 S +753 0 3 Vande Velde, Mr. Johannes Joseph male 33 0 0 345780 9.5 S +754 0 3 Jonkoff, Mr. Lalio male 23 0 0 349204 7.8958 S +755 1 2 Herman, Mrs. Samuel (Jane Laver) female 48 1 2 220845 65 S +756 1 2 Hamalainen, Master. Viljo male 0.67 1 1 250649 14.5 S +757 0 3 Carlsson, Mr. August Sigfrid male 28 0 0 350042 7.7958 S +758 0 2 Bailey, Mr. Percy Andrew male 18 0 0 29108 11.5 S +759 0 3 Theobald, Mr. Thomas Leonard male 34 0 0 363294 8.05 S +760 1 1 Rothes, the Countess. of (Lucy Noel Martha Dyer-Edwards) female 33 0 0 110152 86.5 B77 S +761 0 3 Garfirth, Mr. John male 0 0 358585 14.5 S +762 0 3 Nirva, Mr. Iisakki Antino Aijo male 41 0 0 SOTON/O2 3101272 7.125 S +763 1 3 Barah, Mr. Hanna Assi male 20 0 0 2663 7.2292 C +764 1 1 Carter, Mrs. William Ernest (Lucile Polk) female 36 1 2 113760 120 B96 B98 S +765 0 3 Eklund, Mr. Hans Linus male 16 0 0 347074 7.775 S +766 1 1 Hogeboom, Mrs. John C (Anna Andrews) female 51 1 0 13502 77.9583 D11 S +767 0 1 Brewe, Dr. Arthur Jackson male 0 0 112379 39.6 C +768 0 3 Mangan, Miss. Mary female 30.5 0 0 364850 7.75 Q +769 0 3 Moran, Mr. Daniel J male 1 0 371110 24.15 Q +770 0 3 Gronnestad, Mr. Daniel Danielsen male 32 0 0 8471 8.3625 S +771 0 3 Lievens, Mr. Rene Aime male 24 0 0 345781 9.5 S +772 0 3 Jensen, Mr. Niels Peder male 48 0 0 350047 7.8542 S +773 0 2 Mack, Mrs. (Mary) female 57 0 0 S.O./P.P. 3 10.5 E77 S +774 0 3 Elias, Mr. Dibo male 0 0 2674 7.225 C +775 1 2 Hocking, Mrs. Elizabeth (Eliza Needs) female 54 1 3 29105 23 S +776 0 3 Myhrman, Mr. Pehr Fabian Oliver Malkolm male 18 0 0 347078 7.75 S +777 0 3 Tobin, Mr. Roger male 0 0 383121 7.75 F38 Q +778 1 3 Emanuel, Miss. Virginia Ethel female 5 0 0 364516 12.475 S +779 0 3 Kilgannon, Mr. Thomas J male 0 0 36865 7.7375 Q +780 1 1 Robert, Mrs. Edward Scott (Elisabeth Walton McMillan) female 43 0 1 24160 211.3375 B3 S +781 1 3 Ayoub, Miss. Banoura female 13 0 0 2687 7.2292 C +782 1 1 Dick, Mrs. Albert Adrian (Vera Gillespie) female 17 1 0 17474 57 B20 S +783 0 1 Long, Mr. Milton Clyde male 29 0 0 113501 30 D6 S +784 0 3 Johnston, Mr. Andrew G male 1 2 W./C. 6607 23.45 S +785 0 3 Ali, Mr. William male 25 0 0 SOTON/O.Q. 3101312 7.05 S +786 0 3 Harmer, Mr. Abraham (David Lishin) male 25 0 0 374887 7.25 S +787 1 3 Sjoblom, Miss. Anna Sofia female 18 0 0 3101265 7.4958 S +788 0 3 Rice, Master. George Hugh male 8 4 1 382652 29.125 Q +789 1 3 Dean, Master. Bertram Vere male 1 1 2 C.A. 2315 20.575 S +790 0 1 Guggenheim, Mr. Benjamin male 46 0 0 PC 17593 79.2 B82 B84 C +791 0 3 "Keane, Mr. Andrew ""Andy""" male 0 0 12460 7.75 Q +792 0 2 Gaskell, Mr. Alfred male 16 0 0 239865 26 S +793 0 3 Sage, Miss. Stella Anna female 8 2 CA. 2343 69.55 S +794 0 1 Hoyt, Mr. William Fisher male 0 0 PC 17600 30.6958 C +795 0 3 Dantcheff, Mr. Ristiu male 25 0 0 349203 7.8958 S +796 0 2 Otter, Mr. Richard male 39 0 0 28213 13 S +797 1 1 Leader, Dr. Alice (Farnham) female 49 0 0 17465 25.9292 D17 S +798 1 3 Osman, Mrs. Mara female 31 0 0 349244 8.6833 S +799 0 3 Ibrahim Shawah, Mr. Yousseff male 30 0 0 2685 7.2292 C +800 0 3 Van Impe, Mrs. Jean Baptiste (Rosalie Paula Govaert) female 30 1 1 345773 24.15 S +801 0 2 Ponesell, Mr. Martin male 34 0 0 250647 13 S +802 1 2 Collyer, Mrs. Harvey (Charlotte Annie Tate) female 31 1 1 C.A. 31921 26.25 S +803 1 1 Carter, Master. William Thornton II male 11 1 2 113760 120 B96 B98 S +804 1 3 Thomas, Master. Assad Alexander male 0.42 0 1 2625 8.5167 C +805 1 3 Hedman, Mr. Oskar Arvid male 27 0 0 347089 6.975 S +806 0 3 Johansson, Mr. Karl Johan male 31 0 0 347063 7.775 S +807 0 1 Andrews, Mr. Thomas Jr male 39 0 0 112050 0 A36 S +808 0 3 Pettersson, Miss. Ellen Natalia female 18 0 0 347087 7.775 S +809 0 2 Meyer, Mr. August male 39 0 0 248723 13 S +810 1 1 Chambers, Mrs. Norman Campbell (Bertha Griggs) female 33 1 0 113806 53.1 E8 S +811 0 3 Alexander, Mr. William male 26 0 0 3474 7.8875 S +812 0 3 Lester, Mr. James male 39 0 0 A/4 48871 24.15 S +813 0 2 Slemen, Mr. Richard James male 35 0 0 28206 10.5 S +814 0 3 Andersson, Miss. Ebba Iris Alfrida female 6 4 2 347082 31.275 S +815 0 3 Tomlin, Mr. Ernest Portage male 30.5 0 0 364499 8.05 S +816 0 1 Fry, Mr. Richard male 0 0 112058 0 B102 S +817 0 3 Heininen, Miss. Wendla Maria female 23 0 0 STON/O2. 3101290 7.925 S +818 0 2 Mallet, Mr. Albert male 31 1 1 S.C./PARIS 2079 37.0042 C +819 0 3 Holm, Mr. John Fredrik Alexander male 43 0 0 C 7075 6.45 S +820 0 3 Skoog, Master. Karl Thorsten male 10 3 2 347088 27.9 S +821 1 1 Hays, Mrs. Charles Melville (Clara Jennings Gregg) female 52 1 1 12749 93.5 B69 S +822 1 3 Lulic, Mr. Nikola male 27 0 0 315098 8.6625 S +823 0 1 Reuchlin, Jonkheer. John George male 38 0 0 19972 0 S +824 1 3 Moor, Mrs. (Beila) female 27 0 1 392096 12.475 E121 S +825 0 3 Panula, Master. Urho Abraham male 2 4 1 3101295 39.6875 S +826 0 3 Flynn, Mr. John male 0 0 368323 6.95 Q +827 0 3 Lam, Mr. Len male 0 0 1601 56.4958 S +828 1 2 Mallet, Master. Andre male 1 0 2 S.C./PARIS 2079 37.0042 C +829 1 3 McCormack, Mr. Thomas Joseph male 0 0 367228 7.75 Q +830 1 1 Stone, Mrs. George Nelson (Martha Evelyn) female 62 0 0 113572 80 B28 +831 1 3 Yasbeck, Mrs. Antoni (Selini Alexander) female 15 1 0 2659 14.4542 C +832 1 2 Richards, Master. George Sibley male 0.83 1 1 29106 18.75 S +833 0 3 Saad, Mr. Amin male 0 0 2671 7.2292 C +834 0 3 Augustsson, Mr. Albert male 23 0 0 347468 7.8542 S +835 0 3 Allum, Mr. Owen George male 18 0 0 2223 8.3 S +836 1 1 Compton, Miss. Sara Rebecca female 39 1 1 PC 17756 83.1583 E49 C +837 0 3 Pasic, Mr. Jakob male 21 0 0 315097 8.6625 S +838 0 3 Sirota, Mr. Maurice male 0 0 392092 8.05 S +839 1 3 Chip, Mr. Chang male 32 0 0 1601 56.4958 S +840 1 1 Marechal, Mr. Pierre male 0 0 11774 29.7 C47 C +841 0 3 Alhomaki, Mr. Ilmari Rudolf male 20 0 0 SOTON/O2 3101287 7.925 S +842 0 2 Mudd, Mr. Thomas Charles male 16 0 0 S.O./P.P. 3 10.5 S +843 1 1 Serepeca, Miss. Augusta female 30 0 0 113798 31 C +844 0 3 Lemberopolous, Mr. Peter L male 34.5 0 0 2683 6.4375 C +845 0 3 Culumovic, Mr. Jeso male 17 0 0 315090 8.6625 S +846 0 3 Abbing, Mr. Anthony male 42 0 0 C.A. 5547 7.55 S +847 0 3 Sage, Mr. Douglas Bullen male 8 2 CA. 2343 69.55 S +848 0 3 Markoff, Mr. Marin male 35 0 0 349213 7.8958 C +849 0 2 Harper, Rev. John male 28 0 1 248727 33 S +850 1 1 Goldenberg, Mrs. Samuel L (Edwiga Grabowska) female 1 0 17453 89.1042 C92 C +851 0 3 Andersson, Master. Sigvard Harald Elias male 4 4 2 347082 31.275 S +852 0 3 Svensson, Mr. Johan male 74 0 0 347060 7.775 S +853 0 3 Boulos, Miss. Nourelain female 9 1 1 2678 15.2458 C +854 1 1 Lines, Miss. Mary Conover female 16 0 1 PC 17592 39.4 D28 S +855 0 2 Carter, Mrs. Ernest Courtenay (Lilian Hughes) female 44 1 0 244252 26 S +856 1 3 Aks, Mrs. Sam (Leah Rosen) female 18 0 1 392091 9.35 S +857 1 1 Wick, Mrs. George Dennick (Mary Hitchcock) female 45 1 1 36928 164.8667 S +858 1 1 Daly, Mr. Peter Denis male 51 0 0 113055 26.55 E17 S +859 1 3 Baclini, Mrs. Solomon (Latifa Qurban) female 24 0 3 2666 19.2583 C +860 0 3 Razi, Mr. Raihed male 0 0 2629 7.2292 C +861 0 3 Hansen, Mr. Claus Peter male 41 2 0 350026 14.1083 S +862 0 2 Giles, Mr. Frederick Edward male 21 1 0 28134 11.5 S +863 1 1 Swift, Mrs. Frederick Joel (Margaret Welles Barron) female 48 0 0 17466 25.9292 D17 S +864 0 3 "Sage, Miss. Dorothy Edith ""Dolly""" female 8 2 CA. 2343 69.55 S +865 0 2 Gill, Mr. John William male 24 0 0 233866 13 S +866 1 2 Bystrom, Mrs. (Karolina) female 42 0 0 236852 13 S +867 1 2 Duran y More, Miss. Asuncion female 27 1 0 SC/PARIS 2149 13.8583 C +868 0 1 Roebling, Mr. Washington Augustus II male 31 0 0 PC 17590 50.4958 A24 S +869 0 3 van Melkebeke, Mr. Philemon male 0 0 345777 9.5 S +870 1 3 Johnson, Master. Harold Theodor male 4 1 1 347742 11.1333 S +871 0 3 Balkic, Mr. Cerin male 26 0 0 349248 7.8958 S +872 1 1 Beckwith, Mrs. Richard Leonard (Sallie Monypeny) female 47 1 1 11751 52.5542 D35 S +873 0 1 Carlsson, Mr. Frans Olof male 33 0 0 695 5 B51 B53 B55 S +874 0 3 Vander Cruyssen, Mr. Victor male 47 0 0 345765 9 S +875 1 2 Abelson, Mrs. Samuel (Hannah Wizosky) female 28 1 0 P/PP 3381 24 C +876 1 3 "Najib, Miss. Adele Kiamie ""Jane""" female 15 0 0 2667 7.225 C +877 0 3 Gustafsson, Mr. Alfred Ossian male 20 0 0 7534 9.8458 S +878 0 3 Petroff, Mr. Nedelio male 19 0 0 349212 7.8958 S +879 0 3 Laleff, Mr. Kristo male 0 0 349217 7.8958 S +880 1 1 Potter, Mrs. Thomas Jr (Lily Alexenia Wilson) female 56 0 1 11767 83.1583 C50 C +881 1 2 Shelley, Mrs. William (Imanita Parrish Hall) female 25 0 1 230433 26 S +882 0 3 Markun, Mr. Johann male 33 0 0 349257 7.8958 S +883 0 3 Dahlberg, Miss. Gerda Ulrika female 22 0 0 7552 10.5167 S +884 0 2 Banfield, Mr. Frederick James male 28 0 0 C.A./SOTON 34068 10.5 S +885 0 3 Sutehall, Mr. Henry Jr male 25 0 0 SOTON/OQ 392076 7.05 S +886 0 3 Rice, Mrs. William (Margaret Norton) female 39 0 5 382652 29.125 Q +887 0 2 Montvila, Rev. Juozas male 27 0 0 211536 13 S +888 1 1 Graham, Miss. Margaret Edith female 19 0 0 112053 30 B42 S +889 0 3 "Johnston, Miss. Catherine Helen ""Carrie""" female 1 2 W./C. 6607 23.45 S +890 1 1 Behr, Mr. Karl Howell male 26 0 0 111369 30 C148 C +891 0 3 Dooley, Mr. Patrick male 32 0 0 370376 7.75 Q +892 0 3 Kelly, Mr. James male 34.5 0 0 330911 7.8292 Q +893 1 3 Wilkes, Mrs. James (Ellen Needs) female 47 1 0 363272 7 S +894 0 2 Myles, Mr. Thomas Francis male 62 0 0 240276 9.6875 Q +895 0 3 Wirz, Mr. Albert male 27 0 0 315154 8.6625 S +896 1 3 Hirvonen, Mrs. Alexander (Helga E Lindqvist) female 22 1 1 3101298 12.2875 S +897 0 3 Svensson, Mr. Johan Cervin male 14 0 0 7538 9.225 S +898 1 3 Connolly, Miss. Kate female 30 0 0 330972 7.6292 Q +899 0 2 Caldwell, Mr. Albert Francis male 26 1 1 248738 29 S +900 1 3 Abrahim, Mrs. Joseph (Sophie Halaut Easu) female 18 0 0 2657 7.2292 C +901 0 3 Davies, Mr. John Samuel male 21 2 0 A/4 48871 24.15 S +902 0 3 Ilieff, Mr. Ylio male 0 0 349220 7.8958 S +903 0 1 Jones, Mr. Charles Cresson male 46 0 0 694 26 S +904 1 1 Snyder, Mrs. John Pillsbury (Nelle Stevenson) female 23 1 0 21228 82.2667 B45 S +905 0 2 Howard, Mr. Benjamin male 63 1 0 24065 26 S +906 1 1 Chaffee, Mrs. Herbert Fuller (Carrie Constance Toogood) female 47 1 0 W.E.P. 5734 61.175 E31 S +907 1 2 del Carlo, Mrs. Sebastiano (Argenia Genovesi) female 24 1 0 SC/PARIS 2167 27.7208 C +908 0 2 Keane, Mr. Daniel male 35 0 0 233734 12.35 Q +909 0 3 Assaf, Mr. Gerios male 21 0 0 2692 7.225 C +910 1 3 Ilmakangas, Miss. Ida Livija female 27 1 0 STON/O2. 3101270 7.925 S +911 1 3 "Assaf Khalil, Mrs. Mariana (Miriam"")""" female 45 0 0 2696 7.225 C +912 0 1 Rothschild, Mr. Martin male 55 1 0 PC 17603 59.4 C +913 0 3 Olsen, Master. Artur Karl male 9 0 1 C 17368 3.1708 S +914 1 1 Flegenheim, Mrs. Alfred (Antoinette) female 0 0 PC 17598 31.6833 S +915 0 1 Williams, Mr. Richard Norris II male 21 0 1 PC 17597 61.3792 C +916 1 1 Ryerson, Mrs. Arthur Larned (Emily Maria Borie) female 48 1 3 PC 17608 262.375 B57 B59 B63 B66 C +917 0 3 Robins, Mr. Alexander A male 50 1 0 A/5. 3337 14.5 S +918 1 1 Ostby, Miss. Helene Ragnhild female 22 0 1 113509 61.9792 B36 C +919 0 3 Daher, Mr. Shedid male 22.5 0 0 2698 7.225 C +920 0 1 Brady, Mr. John Bertram male 41 0 0 113054 30.5 A21 S +921 0 3 Samaan, Mr. Elias male 2 0 2662 21.6792 C +922 0 2 Louch, Mr. Charles Alexander male 50 1 0 SC/AH 3085 26 S +923 0 2 Jefferys, Mr. Clifford Thomas male 24 2 0 C.A. 31029 31.5 S +924 1 3 Dean, Mrs. Bertram (Eva Georgetta Light) female 33 1 2 C.A. 2315 20.575 S +925 1 3 "Johnston, Mrs. Andrew G (Elizabeth Lily"" Watson)""" female 1 2 W./C. 6607 23.45 S +926 0 1 Mock, Mr. Philipp Edmund male 30 1 0 13236 57.75 C78 C +927 0 3 "Katavelas, Mr. Vassilios (Catavelas Vassilios"")""" male 18.5 0 0 2682 7.2292 C +928 1 3 Roth, Miss. Sarah A female 0 0 342712 8.05 S +929 1 3 Cacic, Miss. Manda female 21 0 0 315087 8.6625 S +930 0 3 Sap, Mr. Julius male 25 0 0 345768 9.5 S +931 0 3 Hee, Mr. Ling male 0 0 1601 56.4958 S +932 0 3 Karun, Mr. Franz male 39 0 1 349256 13.4167 C +933 0 1 Franklin, Mr. Thomas Parham male 0 0 113778 26.55 D34 S +934 0 3 Goldsmith, Mr. Nathan male 41 0 0 SOTON/O.Q. 3101263 7.85 S +935 1 2 Corbett, Mrs. Walter H (Irene Colvin) female 30 0 0 237249 13 S +936 1 1 Kimball, Mrs. Edwin Nelson Jr (Gertrude Parsons) female 45 1 0 11753 52.5542 D19 S +937 0 3 Peltomaki, Mr. Nikolai Johannes male 25 0 0 STON/O 2. 3101291 7.925 S +938 0 1 Chevre, Mr. Paul Romaine male 45 0 0 PC 17594 29.7 A9 C +939 0 3 Shaughnessy, Mr. Patrick male 0 0 370374 7.75 Q +940 1 1 Bucknell, Mrs. William Robert (Emma Eliza Ward) female 60 0 0 11813 76.2917 D15 C +941 1 3 "Coutts, Mrs. William (Winnie Minnie"" Treanor)""" female 36 0 2 C.A. 37671 15.9 S +942 0 1 Smith, Mr. Lucien Philip male 24 1 0 13695 60 C31 S +943 0 2 Pulbaum, Mr. Franz male 27 0 0 SC/PARIS 2168 15.0333 C +944 1 2 "Hocking, Miss. Ellen Nellie""""" female 20 2 1 29105 23 S +945 1 1 Fortune, Miss. Ethel Flora female 28 3 2 19950 263 C23 C25 C27 S +946 0 2 Mangiavacchi, Mr. Serafino Emilio male 0 0 SC/A.3 2861 15.5792 C +947 0 3 Rice, Master. Albert male 10 4 1 382652 29.125 Q +948 0 3 Cor, Mr. Bartol male 35 0 0 349230 7.8958 S +949 0 3 Abelseth, Mr. Olaus Jorgensen male 25 0 0 348122 7.65 F G63 S +950 0 3 Davison, Mr. Thomas Henry male 1 0 386525 16.1 S +951 1 1 Chaudanson, Miss. Victorine female 36 0 0 PC 17608 262.375 B61 C +952 0 3 Dika, Mr. Mirko male 17 0 0 349232 7.8958 S +953 0 2 McCrae, Mr. Arthur Gordon male 32 0 0 237216 13.5 S +954 0 3 Bjorklund, Mr. Ernst Herbert male 18 0 0 347090 7.75 S +955 1 3 Bradley, Miss. Bridget Delia female 22 0 0 334914 7.725 Q +956 0 1 Ryerson, Master. John Borie male 13 2 2 PC 17608 262.375 B57 B59 B63 B66 C +957 1 2 Corey, Mrs. Percy C (Mary Phyllis Elizabeth Miller) female 0 0 F.C.C. 13534 21 S +958 1 3 Burns, Miss. Mary Delia female 18 0 0 330963 7.8792 Q +959 0 1 Moore, Mr. Clarence Bloomfield male 47 0 0 113796 42.4 S +960 0 1 Tucker, Mr. Gilbert Milligan Jr male 31 0 0 2543 28.5375 C53 C +961 1 1 Fortune, Mrs. Mark (Mary McDougald) female 60 1 4 19950 263 C23 C25 C27 S +962 1 3 Mulvihill, Miss. Bertha E female 24 0 0 382653 7.75 Q +963 0 3 Minkoff, Mr. Lazar male 21 0 0 349211 7.8958 S +964 1 3 Nieminen, Miss. Manta Josefina female 29 0 0 3101297 7.925 S +965 0 1 Ovies y Rodriguez, Mr. Servando male 28.5 0 0 PC 17562 27.7208 D43 C +966 1 1 Geiger, Miss. Amalie female 35 0 0 113503 211.5 C130 C +967 0 1 Keeping, Mr. Edwin male 32.5 0 0 113503 211.5 C132 C +968 0 3 Miles, Mr. Frank male 0 0 359306 8.05 S +969 1 1 Cornell, Mrs. Robert Clifford (Malvina Helen Lamson) female 55 2 0 11770 25.7 C101 S +970 0 2 Aldworth, Mr. Charles Augustus male 30 0 0 248744 13 S +971 1 3 Doyle, Miss. Elizabeth female 24 0 0 368702 7.75 Q +972 0 3 Boulos, Master. Akar male 6 1 1 2678 15.2458 C +973 0 1 Straus, Mr. Isidor male 67 1 0 PC 17483 221.7792 C55 C57 S +974 0 1 Case, Mr. Howard Brown male 49 0 0 19924 26 S +975 0 3 Demetri, Mr. Marinko male 0 0 349238 7.8958 S +976 0 2 Lamb, Mr. John Joseph male 0 0 240261 10.7083 Q +977 0 3 Khalil, Mr. Betros male 1 0 2660 14.4542 C +978 1 3 Barry, Miss. Julia female 27 0 0 330844 7.8792 Q +979 1 3 Badman, Miss. Emily Louisa female 18 0 0 A/4 31416 8.05 S +980 1 3 O'Donoghue, Ms. Bridget female 0 0 364856 7.75 Q +981 0 2 Wells, Master. Ralph Lester male 2 1 1 29103 23 S +982 1 3 Dyker, Mrs. Adolf Fredrik (Anna Elisabeth Judith Andersson) female 22 1 0 347072 13.9 S +983 0 3 Pedersen, Mr. Olaf male 0 0 345498 7.775 S +984 1 1 Davidson, Mrs. Thornton (Orian Hays) female 27 1 2 F.C. 12750 52 B71 S +985 0 3 Guest, Mr. Robert male 0 0 376563 8.05 S +986 0 1 Birnbaum, Mr. Jakob male 25 0 0 13905 26 C +987 0 3 Tenglin, Mr. Gunnar Isidor male 25 0 0 350033 7.7958 S +988 1 1 Cavendish, Mrs. Tyrell William (Julia Florence Siegel) female 76 1 0 19877 78.85 C46 S +989 0 3 Makinen, Mr. Kalle Edvard male 29 0 0 STON/O 2. 3101268 7.925 S +990 1 3 Braf, Miss. Elin Ester Maria female 20 0 0 347471 7.8542 S +991 0 3 Nancarrow, Mr. William Henry male 33 0 0 A./5. 3338 8.05 S +992 1 1 Stengel, Mrs. Charles Emil Henry (Annie May Morris) female 43 1 0 11778 55.4417 C116 C +993 0 2 Weisz, Mr. Leopold male 27 1 0 228414 26 S +994 0 3 Foley, Mr. William male 0 0 365235 7.75 Q +995 0 3 Johansson Palmquist, Mr. Oskar Leander male 26 0 0 347070 7.775 S +996 1 3 "Thomas, Mrs. Alexander (Thamine Thelma"")""" female 16 1 1 2625 8.5167 C +997 0 3 Holthen, Mr. Johan Martin male 28 0 0 C 4001 22.525 S +998 0 3 Buckley, Mr. Daniel male 21 0 0 330920 7.8208 Q +999 0 3 Ryan, Mr. Edward male 0 0 383162 7.75 Q +1000 0 3 "Willer, Mr. Aaron (Abi Weller"")""" male 0 0 3410 8.7125 S +1001 0 2 Swane, Mr. George male 18.5 0 0 248734 13 F S +1002 0 2 Stanton, Mr. Samuel Ward male 41 0 0 237734 15.0458 C +1003 1 3 Shine, Miss. Ellen Natalia female 0 0 330968 7.7792 Q +1004 1 1 Evans, Miss. Edith Corse female 36 0 0 PC 17531 31.6792 A29 C +1005 1 3 Buckley, Miss. Katherine female 18.5 0 0 329944 7.2833 Q +1006 1 1 Straus, Mrs. Isidor (Rosalie Ida Blun) female 63 1 0 PC 17483 221.7792 C55 C57 S +1007 0 3 Chronopoulos, Mr. Demetrios male 18 1 0 2680 14.4542 C +1008 0 3 Thomas, Mr. John male 0 0 2681 6.4375 C +1009 1 3 Sandstrom, Miss. Beatrice Irene female 1 1 1 PP 9549 16.7 G6 S +1010 0 1 Beattie, Mr. Thomson male 36 0 0 13050 75.2417 C6 C +1011 1 2 Chapman, Mrs. John Henry (Sara Elizabeth Lawry) female 29 1 0 SC/AH 29037 26 S +1012 1 2 Watt, Miss. Bertha J female 12 0 0 C.A. 33595 15.75 S +1013 0 3 Kiernan, Mr. John male 1 0 367227 7.75 Q +1014 1 1 Schabert, Mrs. Paul (Emma Mock) female 35 1 0 13236 57.75 C28 C +1015 0 3 Carver, Mr. Alfred John male 28 0 0 392095 7.25 S +1016 0 3 Kennedy, Mr. John male 0 0 368783 7.75 Q +1017 1 3 Cribb, Miss. Laura Alice female 17 0 1 371362 16.1 S +1018 0 3 Brobeck, Mr. Karl Rudolf male 22 0 0 350045 7.7958 S +1019 1 3 McCoy, Miss. Alicia female 2 0 367226 23.25 Q +1020 0 2 Bowenur, Mr. Solomon male 42 0 0 211535 13 S +1021 0 3 Petersen, Mr. Marius male 24 0 0 342441 8.05 S +1022 0 3 Spinner, Mr. Henry John male 32 0 0 STON/OQ. 369943 8.05 S +1023 0 1 Gracie, Col. Archibald IV male 53 0 0 113780 28.5 C51 C +1024 1 3 Lefebre, Mrs. Frank (Frances) female 0 4 4133 25.4667 S +1025 0 3 Thomas, Mr. Charles P male 1 0 2621 6.4375 C +1026 0 3 Dintcheff, Mr. Valtcho male 43 0 0 349226 7.8958 S +1027 0 3 Carlsson, Mr. Carl Robert male 24 0 0 350409 7.8542 S +1028 0 3 Zakarian, Mr. Mapriededer male 26.5 0 0 2656 7.225 C +1029 0 2 Schmidt, Mr. August male 26 0 0 248659 13 S +1030 1 3 Drapkin, Miss. Jennie female 23 0 0 SOTON/OQ 392083 8.05 S +1031 0 3 Goodwin, Mr. Charles Frederick male 40 1 6 CA 2144 46.9 S +1032 1 3 Goodwin, Miss. Jessie Allis female 10 5 2 CA 2144 46.9 S +1033 1 1 Daniels, Miss. Sarah female 33 0 0 113781 151.55 S +1034 0 1 Ryerson, Mr. Arthur Larned male 61 1 3 PC 17608 262.375 B57 B59 B63 B66 C +1035 0 2 Beauchamp, Mr. Henry James male 28 0 0 244358 26 S +1036 0 1 "Lindeberg-Lind, Mr. Erik Gustaf (Mr Edward Lingrey"")""" male 42 0 0 17475 26.55 S +1037 0 3 Vander Planke, Mr. Julius male 31 3 0 345763 18 S +1038 0 1 Hilliard, Mr. Herbert Henry male 0 0 17463 51.8625 E46 S +1039 0 3 Davies, Mr. Evan male 22 0 0 SC/A4 23568 8.05 S +1040 0 1 Crafton, Mr. John Bertram male 0 0 113791 26.55 S +1041 0 2 Lahtinen, Rev. William male 30 1 1 250651 26 S +1042 1 1 Earnshaw, Mrs. Boulton (Olive Potter) female 23 0 1 11767 83.1583 C54 C +1043 0 3 Matinoff, Mr. Nicola male 0 0 349255 7.8958 C +1044 0 3 Storey, Mr. Thomas male 60.5 0 0 3701 S +1045 1 3 Klasen, Mrs. (Hulda Kristina Eugenia Lofqvist) female 36 0 2 350405 12.1833 S +1046 0 3 Asplund, Master. Filip Oscar male 13 4 2 347077 31.3875 S +1047 0 3 Duquemin, Mr. Joseph male 24 0 0 S.O./P.P. 752 7.55 S +1048 1 1 Bird, Miss. Ellen female 29 0 0 PC 17483 221.7792 C97 S +1049 1 3 Lundin, Miss. Olga Elida female 23 0 0 347469 7.8542 S +1050 0 1 Borebank, Mr. John James male 42 0 0 110489 26.55 D22 S +1051 1 3 Peacock, Mrs. Benjamin (Edith Nile) female 26 0 2 SOTON/O.Q. 3101315 13.775 S +1052 1 3 Smyth, Miss. Julia female 0 0 335432 7.7333 Q +1053 0 3 Touma, Master. Georges Youssef male 7 1 1 2650 15.2458 C +1054 1 2 Wright, Miss. Marion female 26 0 0 220844 13.5 S +1055 0 3 Pearce, Mr. Ernest male 0 0 343271 7 S +1056 0 2 Peruschitz, Rev. Joseph Maria male 41 0 0 237393 13 S +1057 1 3 Kink-Heilmann, Mrs. Anton (Luise Heilmann) female 26 1 1 315153 22.025 S +1058 0 1 Brandeis, Mr. Emil male 48 0 0 PC 17591 50.4958 B10 C +1059 0 3 Ford, Mr. Edward Watson male 18 2 2 W./C. 6608 34.375 S +1060 1 1 Cassebeer, Mrs. Henry Arthur Jr (Eleanor Genevieve Fosdick) female 0 0 17770 27.7208 C +1061 1 3 Hellstrom, Miss. Hilda Maria female 22 0 0 7548 8.9625 S +1062 0 3 Lithman, Mr. Simon male 0 0 S.O./P.P. 251 7.55 S +1063 0 3 Zakarian, Mr. Ortin male 27 0 0 2670 7.225 C +1064 0 3 Dyker, Mr. Adolf Fredrik male 23 1 0 347072 13.9 S +1065 0 3 Torfa, Mr. Assad male 0 0 2673 7.2292 C +1066 0 3 Asplund, Mr. Carl Oscar Vilhelm Gustafsson male 40 1 5 347077 31.3875 S +1067 1 2 Brown, Miss. Edith Eileen female 15 0 2 29750 39 S +1068 1 2 Sincock, Miss. Maude female 20 0 0 C.A. 33112 36.75 S +1069 0 1 Stengel, Mr. Charles Emil Henry male 54 1 0 11778 55.4417 C116 C +1070 1 2 Becker, Mrs. Allen Oliver (Nellie E Baumgardner) female 36 0 3 230136 39 F4 S +1071 1 1 Compton, Mrs. Alexander Taylor (Mary Eliza Ingersoll) female 64 0 2 PC 17756 83.1583 E45 C +1072 0 2 McCrie, Mr. James Matthew male 30 0 0 233478 13 S +1073 0 1 Compton, Mr. Alexander Taylor Jr male 37 1 1 PC 17756 83.1583 E52 C +1074 1 1 Marvin, Mrs. Daniel Warner (Mary Graham Carmichael Farquarson) female 18 1 0 113773 53.1 D30 S +1075 0 3 Lane, Mr. Patrick male 0 0 7935 7.75 Q +1076 1 1 Douglas, Mrs. Frederick Charles (Mary Helene Baxter) female 27 1 1 PC 17558 247.5208 B58 B60 C +1077 0 2 Maybery, Mr. Frank Hubert male 40 0 0 239059 16 S +1078 1 2 Phillips, Miss. Alice Frances Louisa female 21 0 1 S.O./P.P. 2 21 S +1079 0 3 Davies, Mr. Joseph male 17 2 0 A/4 48873 8.05 S +1080 1 3 Sage, Miss. Ada female 8 2 CA. 2343 69.55 S +1081 0 2 Veal, Mr. James male 40 0 0 28221 13 S +1082 0 2 Angle, Mr. William A male 34 1 0 226875 26 S +1083 0 1 Salomon, Mr. Abraham L male 0 0 111163 26 S +1084 0 3 van Billiard, Master. Walter John male 11.5 1 1 A/5. 851 14.5 S +1085 0 2 Lingane, Mr. John male 61 0 0 235509 12.35 Q +1086 0 2 Drew, Master. Marshall Brines male 8 0 2 28220 32.5 S +1087 0 3 Karlsson, Mr. Julius Konrad Eugen male 33 0 0 347465 7.8542 S +1088 0 1 Spedden, Master. Robert Douglas male 6 0 2 16966 134.5 E34 C +1089 1 3 Nilsson, Miss. Berta Olivia female 18 0 0 347066 7.775 S +1090 0 2 Baimbrigge, Mr. Charles Robert male 23 0 0 C.A. 31030 10.5 S +1091 1 3 Rasmussen, Mrs. (Lena Jacobsen Solvang) female 0 0 65305 8.1125 S +1092 1 3 Murphy, Miss. Nora female 0 0 36568 15.5 Q +1093 0 3 Danbom, Master. Gilbert Sigvard Emanuel male 0.33 0 2 347080 14.4 S +1094 0 1 Astor, Col. John Jacob male 47 1 0 PC 17757 227.525 C62 C64 C +1095 1 2 Quick, Miss. Winifred Vera female 8 1 1 26360 26 S +1096 0 2 Andrew, Mr. Frank Thomas male 25 0 0 C.A. 34050 10.5 S +1097 0 1 Omont, Mr. Alfred Fernand male 0 0 F.C. 12998 25.7417 C +1098 1 3 McGowan, Miss. Katherine female 35 0 0 9232 7.75 Q +1099 0 2 Collett, Mr. Sidney C Stuart male 24 0 0 28034 10.5 S +1100 1 1 Rosenbaum, Miss. Edith Louise female 33 0 0 PC 17613 27.7208 A11 C +1101 0 3 Delalic, Mr. Redjo male 25 0 0 349250 7.8958 S +1102 0 3 Andersen, Mr. Albert Karvin male 32 0 0 C 4001 22.525 S +1103 0 3 Finoli, Mr. Luigi male 0 0 SOTON/O.Q. 3101308 7.05 S +1104 0 2 Deacon, Mr. Percy William male 17 0 0 S.O.C. 14879 73.5 S +1105 1 2 Howard, Mrs. Benjamin (Ellen Truelove Arman) female 60 1 0 24065 26 S +1106 1 3 Andersson, Miss. Ida Augusta Margareta female 38 4 2 347091 7.775 S +1107 0 1 Head, Mr. Christopher male 42 0 0 113038 42.5 B11 S +1108 1 3 Mahon, Miss. Bridget Delia female 0 0 330924 7.8792 Q +1109 0 1 Wick, Mr. George Dennick male 57 1 1 36928 164.8667 S +1110 1 1 Widener, Mrs. George Dunton (Eleanor Elkins) female 50 1 1 113503 211.5 C80 C +1111 0 3 Thomson, Mr. Alexander Morrison male 0 0 32302 8.05 S +1112 1 2 Duran y More, Miss. Florentina female 30 1 0 SC/PARIS 2148 13.8583 C +1113 0 3 Reynolds, Mr. Harold J male 21 0 0 342684 8.05 S +1114 1 2 Cook, Mrs. (Selena Rogers) female 22 0 0 W./C. 14266 10.5 F33 S +1115 0 3 Karlsson, Mr. Einar Gervasius male 21 0 0 350053 7.7958 S +1116 1 1 Candee, Mrs. Edward (Helen Churchill Hungerford) female 53 0 0 PC 17606 27.4458 C +1117 1 3 "Moubarek, Mrs. George (Omine Amenia"" Alexander)""" female 0 2 2661 15.2458 C +1118 0 3 Asplund, Mr. Johan Charles male 23 0 0 350054 7.7958 S +1119 1 3 McNeill, Miss. Bridget female 0 0 370368 7.75 Q +1120 0 3 Everett, Mr. Thomas James male 40.5 0 0 C.A. 6212 15.1 S +1121 0 2 Hocking, Mr. Samuel James Metcalfe male 36 0 0 242963 13 S +1122 0 2 Sweet, Mr. George Frederick male 14 0 0 220845 65 S +1123 1 1 Willard, Miss. Constance female 21 0 0 113795 26.55 S +1124 0 3 Wiklund, Mr. Karl Johan male 21 1 0 3101266 6.4958 S +1125 0 3 Linehan, Mr. Michael male 0 0 330971 7.8792 Q +1126 0 1 Cumings, Mr. John Bradley male 39 1 0 PC 17599 71.2833 C85 C +1127 0 3 Vendel, Mr. Olof Edvin male 20 0 0 350416 7.8542 S +1128 0 1 Warren, Mr. Frank Manley male 64 1 0 110813 75.25 D37 C +1129 0 3 Baccos, Mr. Raffull male 20 0 0 2679 7.225 C +1130 1 2 Hiltunen, Miss. Marta female 18 1 1 250650 13 S +1131 1 1 Douglas, Mrs. Walter Donald (Mahala Dutton) female 48 1 0 PC 17761 106.425 C86 C +1132 1 1 Lindstrom, Mrs. Carl Johan (Sigrid Posse) female 55 0 0 112377 27.7208 C +1133 1 2 Christy, Mrs. (Alice Frances) female 45 0 2 237789 30 S +1134 0 1 Spedden, Mr. Frederic Oakley male 45 1 1 16966 134.5 E34 C +1135 0 3 Hyman, Mr. Abraham male 0 0 3470 7.8875 S +1136 0 3 "Johnston, Master. William Arthur Willie""""" male 1 2 W./C. 6607 23.45 S +1137 0 1 Kenyon, Mr. Frederick R male 41 1 0 17464 51.8625 D21 S +1138 1 2 Karnes, Mrs. J Frank (Claire Bennett) female 22 0 0 F.C.C. 13534 21 S +1139 0 2 Drew, Mr. James Vivian male 42 1 1 28220 32.5 S +1140 1 2 Hold, Mrs. Stephen (Annie Margaret Hill) female 29 1 0 26707 26 S +1141 1 3 "Khalil, Mrs. Betros (Zahie Maria"" Elias)""" female 1 0 2660 14.4542 C +1142 1 2 West, Miss. Barbara J female 0.92 1 2 C.A. 34651 27.75 S +1143 0 3 Abrahamsson, Mr. Abraham August Johannes male 20 0 0 SOTON/O2 3101284 7.925 S +1144 0 1 Clark, Mr. Walter Miller male 27 1 0 13508 136.7792 C89 C +1145 0 3 Salander, Mr. Karl Johan male 24 0 0 7266 9.325 S +1146 0 3 Wenzel, Mr. Linhart male 32.5 0 0 345775 9.5 S +1147 0 3 MacKay, Mr. George William male 0 0 C.A. 42795 7.55 S +1148 0 3 Mahon, Mr. John male 0 0 AQ/4 3130 7.75 Q +1149 0 3 Niklasson, Mr. Samuel male 28 0 0 363611 8.05 S +1150 1 2 Bentham, Miss. Lilian W female 19 0 0 28404 13 S +1151 0 3 Midtsjo, Mr. Karl Albert male 21 0 0 345501 7.775 S +1152 0 3 de Messemaeker, Mr. Guillaume Joseph male 36.5 1 0 345572 17.4 S +1153 0 3 Nilsson, Mr. August Ferdinand male 21 0 0 350410 7.8542 S +1154 1 2 "Wells, Mrs. Arthur Henry (Addie"" Dart Trevaskis)""" female 29 0 2 29103 23 S +1155 1 3 Klasen, Miss. Gertrud Emilia female 1 1 1 350405 12.1833 S +1156 0 2 Portaluppi, Mr. Emilio Ilario Giuseppe male 30 0 0 C.A. 34644 12.7375 C +1157 0 3 Lyntakoff, Mr. Stanko male 0 0 349235 7.8958 S +1158 0 1 Chisholm, Mr. Roderick Robert Crispin male 0 0 112051 0 S +1159 0 3 Warren, Mr. Charles William male 0 0 C.A. 49867 7.55 S +1160 1 3 Howard, Miss. May Elizabeth female 0 0 A. 2. 39186 8.05 S +1161 0 3 Pokrnic, Mr. Mate male 17 0 0 315095 8.6625 S +1162 0 1 McCaffry, Mr. Thomas Francis male 46 0 0 13050 75.2417 C6 C +1163 0 3 Fox, Mr. Patrick male 0 0 368573 7.75 Q +1164 1 1 Clark, Mrs. Walter Miller (Virginia McDowell) female 26 1 0 13508 136.7792 C89 C +1165 1 3 Lennon, Miss. Mary female 1 0 370371 15.5 Q +1166 0 3 Saade, Mr. Jean Nassr male 0 0 2676 7.225 C +1167 1 2 Bryhl, Miss. Dagmar Jenny Ingeborg female 20 1 0 236853 26 S +1168 0 2 Parker, Mr. Clifford Richard male 28 0 0 SC 14888 10.5 S +1169 0 2 Faunthorpe, Mr. Harry male 40 1 0 2926 26 S +1170 0 2 Ware, Mr. John James male 30 1 0 CA 31352 21 S +1171 0 2 Oxenham, Mr. Percy Thomas male 22 0 0 W./C. 14260 10.5 S +1172 1 3 Oreskovic, Miss. Jelka female 23 0 0 315085 8.6625 S +1173 0 3 Peacock, Master. Alfred Edward male 0.75 1 1 SOTON/O.Q. 3101315 13.775 S +1174 1 3 Fleming, Miss. Honora female 0 0 364859 7.75 Q +1175 1 3 Touma, Miss. Maria Youssef female 9 1 1 2650 15.2458 C +1176 1 3 Rosblom, Miss. Salli Helena female 2 1 1 370129 20.2125 S +1177 0 3 Dennis, Mr. William male 36 0 0 A/5 21175 7.25 S +1178 0 3 Franklin, Mr. Charles (Charles Fardon) male 0 0 SOTON/O.Q. 3101314 7.25 S +1179 0 1 Snyder, Mr. John Pillsbury male 24 1 0 21228 82.2667 B45 S +1180 0 3 Mardirosian, Mr. Sarkis male 0 0 2655 7.2292 F E46 C +1181 0 3 Ford, Mr. Arthur male 0 0 A/5 1478 8.05 S +1182 0 1 Rheims, Mr. George Alexander Lucien male 0 0 PC 17607 39.6 S +1183 1 3 "Daly, Miss. Margaret Marcella Maggie""""" female 30 0 0 382650 6.95 Q +1184 0 3 Nasr, Mr. Mustafa male 0 0 2652 7.2292 C +1185 0 1 Dodge, Dr. Washington male 53 1 1 33638 81.8583 A34 S +1186 0 3 Wittevrongel, Mr. Camille male 36 0 0 345771 9.5 S +1187 0 3 Angheloff, Mr. Minko male 26 0 0 349202 7.8958 S +1188 1 2 Laroche, Miss. Louise female 1 1 2 SC/Paris 2123 41.5792 C +1189 0 3 Samaan, Mr. Hanna male 2 0 2662 21.6792 C +1190 0 1 Loring, Mr. Joseph Holland male 30 0 0 113801 45.5 S +1191 0 3 Johansson, Mr. Nils male 29 0 0 347467 7.8542 S +1192 0 3 Olsson, Mr. Oscar Wilhelm male 32 0 0 347079 7.775 S +1193 0 2 Malachard, Mr. Noel male 0 0 237735 15.0458 D C +1194 0 2 Phillips, Mr. Escott Robert male 43 0 1 S.O./P.P. 2 21 S +1195 0 3 Pokrnic, Mr. Tome male 24 0 0 315092 8.6625 S +1196 1 3 "McCarthy, Miss. Catherine Katie""""" female 0 0 383123 7.75 Q +1197 1 1 Crosby, Mrs. Edward Gifford (Catherine Elizabeth Halstead) female 64 1 1 112901 26.55 B26 S +1198 0 1 Allison, Mr. Hudson Joshua Creighton male 30 1 2 113781 151.55 C22 C26 S +1199 0 3 Aks, Master. Philip Frank male 0.83 0 1 392091 9.35 S +1200 0 1 Hays, Mr. Charles Melville male 55 1 1 12749 93.5 B69 S +1201 1 3 Hansen, Mrs. Claus Peter (Jennie L Howard) female 45 1 0 350026 14.1083 S +1202 0 3 Cacic, Mr. Jego Grga male 18 0 0 315091 8.6625 S +1203 0 3 Vartanian, Mr. David male 22 0 0 2658 7.225 C +1204 0 3 Sadowitz, Mr. Harry male 0 0 LP 1588 7.575 S +1205 1 3 Carr, Miss. Jeannie female 37 0 0 368364 7.75 Q +1206 1 1 White, Mrs. John Stuart (Ella Holmes) female 55 0 0 PC 17760 135.6333 C32 C +1207 1 3 Hagardon, Miss. Kate female 17 0 0 AQ/3. 30631 7.7333 Q +1208 0 1 Spencer, Mr. William Augustus male 57 1 0 PC 17569 146.5208 B78 C +1209 0 2 Rogers, Mr. Reginald Harry male 19 0 0 28004 10.5 S +1210 0 3 Jonsson, Mr. Nils Hilding male 27 0 0 350408 7.8542 S +1211 0 2 Jefferys, Mr. Ernest Wilfred male 22 2 0 C.A. 31029 31.5 S +1212 0 3 Andersson, Mr. Johan Samuel male 26 0 0 347075 7.775 S +1213 0 3 Krekorian, Mr. Neshan male 25 0 0 2654 7.2292 F E57 C +1214 0 2 Nesson, Mr. Israel male 26 0 0 244368 13 F2 S +1215 0 1 Rowe, Mr. Alfred G male 33 0 0 113790 26.55 S +1216 1 1 Kreuchen, Miss. Emilie female 39 0 0 24160 211.3375 S +1217 0 3 Assam, Mr. Ali male 23 0 0 SOTON/O.Q. 3101309 7.05 S +1218 1 2 Becker, Miss. Ruth Elizabeth female 12 2 1 230136 39 F4 S +1219 0 1 "Rosenshine, Mr. George (Mr George Thorne"")""" male 46 0 0 PC 17585 79.2 C +1220 0 2 Clarke, Mr. Charles Valentine male 29 1 0 2003 26 S +1221 0 2 Enander, Mr. Ingvar male 21 0 0 236854 13 S +1222 1 2 Davies, Mrs. John Morgan (Elizabeth Agnes Mary White) female 48 0 2 C.A. 33112 36.75 S +1223 0 1 Dulles, Mr. William Crothers male 39 0 0 PC 17580 29.7 A18 C +1224 0 3 Thomas, Mr. Tannous male 0 0 2684 7.225 C +1225 1 3 "Nakid, Mrs. Said (Waika Mary"" Mowad)""" female 19 1 1 2653 15.7417 C +1226 0 3 Cor, Mr. Ivan male 27 0 0 349229 7.8958 S +1227 0 1 Maguire, Mr. John Edward male 30 0 0 110469 26 C106 S +1228 0 2 de Brito, Mr. Jose Joaquim male 32 0 0 244360 13 S +1229 0 3 Elias, Mr. Joseph male 39 0 2 2675 7.2292 C +1230 0 2 Denbury, Mr. Herbert male 25 0 0 C.A. 31029 31.5 S +1231 0 3 Betros, Master. Seman male 0 0 2622 7.2292 C +1232 0 2 Fillbrook, Mr. Joseph Charles male 18 0 0 C.A. 15185 10.5 S +1233 0 3 Lundstrom, Mr. Thure Edvin male 32 0 0 350403 7.5792 S +1234 0 3 Sage, Mr. John George male 1 9 CA. 2343 69.55 S +1235 1 1 Cardeza, Mrs. James Warburton Martinez (Charlotte Wardle Drake) female 58 0 1 PC 17755 512.3292 B51 B53 B55 C +1236 0 3 van Billiard, Master. James William male 1 1 A/5. 851 14.5 S +1237 1 3 Abelseth, Miss. Karen Marie female 16 0 0 348125 7.65 S +1238 0 2 Botsford, Mr. William Hull male 26 0 0 237670 13 S +1239 1 3 Whabee, Mrs. George Joseph (Shawneene Abi-Saab) female 38 0 0 2688 7.2292 C +1240 0 2 Giles, Mr. Ralph male 24 0 0 248726 13.5 S +1241 1 2 Walcroft, Miss. 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Michael J male 1 1 2668 22.3583 C diff --git a/data/winequality-red.csv b/data/winequality-red.csv new file mode 100644 index 0000000..9bb4e3c --- /dev/null +++ b/data/winequality-red.csv @@ -0,0 +1,1600 @@ +"fixed acidity";"volatile acidity";"citric acid";"residual sugar";"chlorides";"free sulfur dioxide";"total sulfur dioxide";"density";"pH";"sulphates";"alcohol";"quality" +7.4;0.7;0;1.9;0.076;11;34;0.9978;3.51;0.56;9.4;5 +7.8;0.88;0;2.6;0.098;25;67;0.9968;3.2;0.68;9.8;5 +7.8;0.76;0.04;2.3;0.092;15;54;0.997;3.26;0.65;9.8;5 +11.2;0.28;0.56;1.9;0.075;17;60;0.998;3.16;0.58;9.8;6 +7.4;0.7;0;1.9;0.076;11;34;0.9978;3.51;0.56;9.4;5 +7.4;0.66;0;1.8;0.075;13;40;0.9978;3.51;0.56;9.4;5 +7.9;0.6;0.06;1.6;0.069;15;59;0.9964;3.3;0.46;9.4;5 +7.3;0.65;0;1.2;0.065;15;21;0.9946;3.39;0.47;10;7 +7.8;0.58;0.02;2;0.073;9;18;0.9968;3.36;0.57;9.5;7 +7.5;0.5;0.36;6.1;0.071;17;102;0.9978;3.35;0.8;10.5;5 +6.7;0.58;0.08;1.8;0.097;15;65;0.9959;3.28;0.54;9.2;5 +7.5;0.5;0.36;6.1;0.071;17;102;0.9978;3.35;0.8;10.5;5 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+cycler==0.12.1 +debugpy==1.8.17 +decorator==5.2.1 +executing==2.2.1 +fonttools==4.60.1 +formulaic==1.2.1 +interface-meta==1.3.0 +ipykernel==7.1.0 +ipython==9.6.0 +ipython_pygments_lexers==1.1.1 +jedi==0.19.2 +jupyter_client==8.6.3 +jupyter_core==5.9.1 +kiwisolver==1.4.9 +lifelines==0.30.0 +matplotlib==3.10.7 +matplotlib-inline==0.2.1 +narwhals==2.11.0 +nest-asyncio==1.6.0 +numdifftools==0.9.41 +numpy==2.3.4 +packaging==25.0 +pandas==2.3.3 +parso==0.8.5 +patsy==1.0.2 +pillow==12.0.0 +platformdirs==4.5.0 +prompt_toolkit==3.0.52 +psutil==7.1.2 +pure_eval==0.2.3 +Pygments==2.19.2 +pyparsing==3.2.5 +python-dateutil==2.9.0.post0 +pytz==2025.2 +pyzmq==27.1.0 +scipy==1.16.3 +seaborn==0.13.2 +six==1.17.0 +stack-data==0.6.3 +statsmodels==0.14.5 +tornado==6.5.2 +traitlets==5.14.3 +typing_extensions==4.15.0 +tzdata==2025.2 +wcwidth==0.2.14 +wrapt==2.0.1 diff --git a/src/Course_part_1/basic_stat_1.ipynb b/src/Course_part_1/basic_stat_1.ipynb new file mode 100644 index 0000000..65a6438 --- /dev/null +++ b/src/Course_part_1/basic_stat_1.ipynb @@ -0,0 +1,2201 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# Основы статистики\n", + "\n", + "## Конспект лекций\n", + "\n", + "Автор лекций: **Анатолий Карпов**\n", + "\n", + "Конспектировал: отрок Михаил Курочкин\n", + "\n", + "telegram: @mikhail_kurochkin\n", + "instagram: mikhail_k17 если хотите вообще от души поблагодарить - подписка/лайк :)\n", + "\n", + "Дополнял: отрок Илья Дашков" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Содержание\n", + "### Неделя 1\n", + " - [Генеральная совокупность и выборка](#Генеральная-совокупность-и-выборка)\n", + " - [Типы переменных](#Типы-переменных)\n", + " - [Описательная статистика](#Описательная-статистика)\n", + " - [Меры центральной тенденции](#Меры-центральной-тенденции)\n", + " - [Мода](#Мода)\n", + " - [Медиана](#Медиана)\n", + " - [Среднее значение](#Среднее-значение)\n", + " - [Примеры](#1.Примеры)\n", + " - [Меры изменчивости](#Меры-изменчивости)\n", + " - [Размах](#Размах)\n", + " - [Дисперсия](#Дисперсия)\n", + " - [Квартили распределения](#Квартили-распределения)\n", + " - [Пример](#2.Пример)\n", + " - [Нормальное распределение](#Нормальное-распределение)\n", + " - [Z-преобразование](#Z-преобразование)\n", + " - [Правило 3х-сигм](#Правило-3х-сигм)\n", + " - [Примеры](#3.Примеры)\n", + " - [Центральная предельная теорема](#Центральная-предельная-теорема)\n", + " - [Примеры](#4.Примеры)\n", + " - [Доверительные интервалы для среднего](#Доверительные-интервалы-для-среднего)\n", + " - [Идея статистического вывода](#Идея-статистического-вывода)\n", + " - [Статистическая проверка гипотез](#Статистическая-проверка-гипотез)\n", + " - [p-уровень значимости](#p-уровень-значимости)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Неделя 2\n", + " - [T-распределение](#T-распределение)\n", + " - [Подробно про нормальное и t-распредление](#Подробно-про-нормальное-и-t-распредление)\n", + " - [Примеры](#5.Примеры)\n", + " - [Сравнение двух средних; t-критерий Стьюдента](#Сравнение-двух-средних.-t-критерий-Стьюдента)\n", + " - [Примеры применения t-критерий Стьюдента](#Примеры-применения-t-критерий-Стьюдента)\n", + " - [Построение графиков](#6.-Примеры)\n", + " - [Проверка распределения на нормальность](#Проверка-распределения-на-нормальность)\n", + " - [QQ-plot](#QQ-plot)\n", + " - [Примеры](#Примеры)\n", + " - [Однофакторный дисперсионный анализ](#Однофакторный-дисперсионный-анализ)\n", + " - [Множественные сравнения в ANOVA](#Множественные-сравнения-в-ANOVA)\n", + " - [почему мы не можем применить t-критерий для более двух выборок](#почему-мы-не-можем-применить-t-критерий-для-более-двух-выборок)\n", + " - [Многофакторный ANOVA](#Многофакторный-ANOVA)\n", + " - [Двухфакторный дисперсионный анализ](#Двухфакторный-дисперсионный-анализ)\n", + " - [Взаимодействие факторов в ANOVA](#Взаимодействие-факторов-в-ANOVA)\n", + " - [Требования к данным](#Требования-к-данным)\n", + " - [Интерпрертация результатов](#Интерпрертация-результатов)\n", + " - [АБ тесты и статистика](#АБ-тесты-и-статистика)\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Неделя 3\n", + "\n", + " - [Корреляция](#Корреляция)\n", + " - [Ковариация](#Ковариация)\n", + " - [Примеры](#Примеры-3.1)\n", + " - [Регрессия с одной независимой переменной](#Регрессия-с-одной-независимой-переменной)\n", + " - [Гипотеза о значимости взаимосвязи и коэффициент детерминации](#Гипотеза-о-значимости-взаимосвязи-и-коэффициент-детерминации)\n", + " - [Условия применения линейной регрессии с одним предиктором](#Условия-применения-линейной-регрессии-с-одним-предиктором)\n", + " - [Задача предсказания значений зависимой переменной](#Задача-предсказания-значений-зависимой-переменной)\n", + " - [Регрессионный анализ с несколькими независимыми переменными](#Регрессионный-анализ-с-несколькими-независимыми-переменными)\n", + " - [Пример расчёта и визуализации множественной регрессии](#Пример-расчёта-и-визуализации-множественной-регрессии)\n", + " - [Выбор наилучшей модели](#Выбор-наилучшей-модели)\n", + " - [Классификация: логистическая регрессия и кластерный анализ](#Классификация:-логистическая-регрессия-и-кластерный-анализ)\n", + " - [GLM и продвинутые темы](##GLM-и-продвинутые-темы)\n", + " - [Заключение](##Заключение)\n", + "\n", + "\n", + "[Полезные ссылки](#Полезные-ссылки)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Часть 1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Генеральная совокупность и выборка\n", + " - **Генеральная совокупность** (от лат. generis — общий, родовой) — совокупность всех объектов, относительно которых предполагается делать выводы при изучении конкретной задачи. Далее ГС.\n", + " - **Репрезентативная выборка** – это такая выборка, в которой все основные признаки генеральной совокупности, из которой извлечена данная выборка, представлены приблизительно в той же пропорции или с той же частотой, с которой данный признак выступает в этой генеральной совокупности.\n", + "\n", + "### Способы репрезентативной выборки:\n", + " - **Простая случайная выборка** (simple random sample)\n", + " - **Стратифицированная выборка** (stratified sample) – разделение ГС на страты (группы) а оттуда уже делается случайная выборка.\n", + " - **Групповая выборка** (cluster sample) – похожие группы выбираются из выборки и далее делается случайная выборка (например, районы одного города)\n", + " \n", + "| групповая выборка | Стратифицированная выборка |\n", + "|----------------------------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------------------|\n", + "| Выборка формируется только из несколько субпопуляций (кластеров) | Выборка формируется из всех субпопуляций (страт) |\n", + "| В пределах кластера элементы должны быть разнородны, тогда как поддерживается однородность или схожесть между разными кластерами | В пределах страты элементы должны быть однородны, а между стратами должна быть разнородность (различия) |\n", + "| Схема выборки нужна только для кластеров, попавших в выборку | Должна быть сформирована полная схема выборки для всех стратифицированных субпопуляций |\n", + "| Повышает эффективность выборки, уменьшая стоимость | Повышает точность |\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Типы переменных\n", + "\n", + " * **Количественные** – измеряемое (например, рост):\n", + " + **Непрерывные** – переменная принимает любое значение на опр. промежутке;\n", + " + **Дискретные** – только определенные значения (3.5 ребенка в семье не будет).\n", + " * **Номинативные (качественные)** – разделение испытуемых на группы, цифры как маркеры (например: 1 -женщины, 2 – мужчины). Цифры используются как имена групп, они не предназначены для расчётов. \n", + " * **Ранговые** – похоже на номинативные, только возможны сравнения (быстрее/медленнее и т.п.)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Описательная статистика\n", + "### Глоссарий:\n", + " - **Эмпирические данные** - данные полученные опытным путём.\n", + "\n", + " - **Описательная (дескриптивная) статистика** - обработка данных полученных эмпирическим путём и их систематизация, наглядное представление в форме графиков, таблиц, а также их количественное описание посредством основных статистических показателей.\n", + "\n", + " - **Распределение вероятностей** - это закон, описывающий область значений случайной величины и вероятность её появления (частоту) в данной области. То есть насколько часто X появляется в данном диапазоне значений.\n", + "\n", + " - **Гистограмма частот** - ступенчатая функция показывающая насколько часто вероятно появление величины в указанном диапазоне значений.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Меры центральной тенденции\n", + "### Мода\n", + "Это значение признака, которое встречается максимально часто. В выборке может быть несколько мод или одна мода.\n", + "### Медиана\n", + "Это значение признака, которое делит упорядочное множество пополам. Если множество содержит чётное количество элементов, то берётся среднее из двух серединных элементов упорядочного множества.\n", + "### Среднее значение\n", + "Cумма всех значений измеренного признака делится на количество измеренных значений.\n", + "\n", + "#### Свойства среднего значения\n", + "$$M_{x + c} = \\frac{\\sum_{i=1}^{n}{(x_{i} + c)}}{n} = \\frac{\\sum_{i=1}^{n} x_{i}}{n} + \\frac{\\sum_{i=1}^{n} c}{n} = M_{x} + \\frac{nc}{n} = M_{x} + c$$\n", + "\n", + "$$M_{x * c} = \\frac{\\sum_{i=1}^{n}{(x_{i} * c)}}{n} = \\frac{c * \\sum_{i=1}^{n} x_{i}}{n} = c * M_{x}$$\n", + "\n", + "$$\\sum_{i=1}^{n} (x_{i} - M_{x}) = nM_{x} - nM_{x} = 0$$\n", + "\n", + "### 1.Примеры " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "'''Расчёт моды, медианы и среднего с помощью библиотек numpy и scipy'''\n", + "import numpy as np\n", + "from scipy import stats\n", + "sample = np.array([185, 175, 170, 169, 171, 175, 157, 172, 170, 172, 167, 173, 168, 167, 166,\n", + " 167, 169, 172, 177, 178, 165, 161, 179, 159, 164, 178, 172, 170, 173, 171])\n", + "mode = stats.mode(sample)\n", + "# в numpy почему-то нет моды\n", + "print('Мода:', mode[0])\n", + "print('Медиана:', np.median(sample))\n", + "print('Среднее:', np.mean(sample))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "'''Расчёт моды, медианы и среднего с помощью библиотеки pandas'''\n", + "import pandas as pd\n", + "import numpy as np\n", + "sample = pd.Series([185, 175, 170, 169, 171, 175, 157, 172, 170, 172, 167, 173, 168, 167, 166,\n", + " 167, 169, 172, 177, 178, 165, 161, 179, 159, 164, 178, 172, 170, 173, 171])\n", + "mode = np.array(sample.mode().array)\n", + "print('mode:', mode)\n", + "print('median:', sample.median())\n", + "print('mean:', sample.mean())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Меры изменчивости\n", + "### Размах\n", + "Это разность между максимальным и минимальным значениям выборки. Крайне чувствителен к взбросам.\n", + "### Дисперсия\n", + "\n", + "Это средний квадрат отклонений индивидуальных значений признака от их средней величины\n", + "\n", + "#### Для генеральной совокупности\n", + "$$D = \\frac{\\sum_{i=1}^{n} (x_{i} - M_{x})^2}{n}$$\n", + "Среднеквадратическое отклонение\n", + "$$ \\sigma = \\sqrt{D}$$\n", + "#### Для выборки\n", + "$$D = \\frac{\\sum_{i=1}^{n} (x_{i} - M_{x})^2}{n-1}$$\n", + "где 1 это количество степеней свободы\n", + "Важно отменить, что среднеквадратическое отклонение для выборки обозначают по другому, как **sd** - standart deviation\n", + "\n", + "#### Ликбез: Почему именно квадрат, а не модуль или куб?\n", + " Могу предположить, что линейное отклонение более чувствительно выбросам, квадратичное менее, кубическое — ещё менее чувствительно.\n", + " Попробовал посчитать для 3-х выборок: [1,2,3,4,5], [1,2,3,4,50] и [1,2,3,4,500]:\n", + "\n", + " - Линейное: 2.5, 452.5 и 49502.5\n", + " - Квадратичное: 1.58, 21.27 и 222.49\n", + " - Кубическое: 1.36, 7.68, и 36.71\n", + " \n", + "Модуль не берут потому, что модуль - не гладкая функция. В нуле у модуля имеется \"излом\" из-за которого у производной происходит разрыв.\n", + "А очень многие математические теоремы, которые наверняка потребуются дальше, работают только на гладких функциях.\n", + "\n", + "Вообще, с не гладкими функциями работать не любят. Там все становится сложнее. Поэтому берется квадрат.\n", + "[Source](#https://stepik.org/lesson/8076/step/5?discussion=49741&unit=1356)\n", + "\n", + "#### Свойства дисперсии\n", + "\n", + "$$ D_{x+c} = D_x $$\n", + "$$ D_{x*c} = D_x+c^2 $$\n", + "\n", + "### Квартили распределения\n", + "**Квартили** - это три точки(значения признака), которые делят **упорядочное** множество данных на 4 равные части.\n", + "\n", + "**Box plot** - такой вид диаграммы в удобной форме показывает медиану, нижний и верхний квартили, минимальное и максимальное значение выборки и выбросы.\n", + "\n", + "\n", + "\n", + "Квартили и inter quartile range используют, чтобы оценить наличие выбросов. Алгоритм расчета - посчитали квартили, посчитали разницу между ними, вычислили теоретический максимум и минимум, сравнили с имеющимся и выяснили есть ли у вас выбросы и сколько их. Если много, то нужно анализировать и решать брать ли их в выборку или нет. \n", + "\n", + "### 2.Пример\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "'''Расчитываем размах и стандартное отклонение с помощью numpy'''\n", + "import numpy as np\n", + "\n", + "sample = np.array([185, 175, 170, 169, 171, 175, 157, 172, 170, 172, 167, 173, 168, 167, 166,\n", + " 167, 169, 172, 177, 178, 165, 161, 179, 159, 164, 178, 172, 170, 173, 171])\n", + "\n", + "# The name of the function comes from the acronym for ‘peak to peak’.\n", + "print(f'Range: {np.ptp(sample)} is equal max - min: {np.max(sample)- np.min(sample)}')\n", + "\n", + "# ddof - Delta Degrees of Freedom\n", + "print(f'Standard deviation: {np.std(sample, ddof=1):.2f}')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Диаграмма boxplot" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "'''с помощью диаграммы boxplot мы можем узнать медиану, 2 и 3 квартиль'''\n", + "import matplotlib.pyplot as plt\n", + "\n", + "#пример графика boxplot\n", + "plt.boxplot(sample, showfliers=1)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Нормальное распределение\n", + "\n", + "$$y = \\frac{1}{\\sigma\\sqrt{2\\pi}} \\cdot e^{-\\frac{1}{2}(\\frac{x-\\mu}{\\sigma})^2}$$\n", + "\n", + " - Унимодально\n", + " - Симметрично\n", + " - Отклонения наблюдений от среднего подчиняются определённому вероятностному закону\n", + " \n", + "\n", + "Нормальное распределение возникает в результате воздействия множества факторов, вклад каждого из которых очень мал.\n", + "\n", + "Для облегчения этого восприятия в 1873 году Фрэнсис Гальтон сделал устройство, которое в последствии назвали Доской Галтона (или квинкункс). Суть простая: сверху по середине подаются шарики, которые при прохождении нескольких уровней (например, 10-ти) на каждом уровне сталкиваются с препятствием, и при каждом столкновении отскакивают либо влево, либо вправо (с равной вероятностью).\n", + "\n", + "Как вы догадываетесь, результатом прохождения - это распределение, стремящееся к нормальному!\n", + "\n", + "Выглядит это так:\n", + "\n", + "\n", + "\n", + "Или в виде кода:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "'''Иммитация доски Гальтона в коде'''\n", + "import seaborn as sns # подключаем библиотеку, модернизирующую mathplotlib для статистики\n", + "\n", + "data = dict() #словарь с набором итоговое положение - кол-во шариков\n", + "N = 10000 # количество шариков\n", + "levels = 20 # количество уровней\n", + "\n", + "for ball in range(N):\n", + " index = 0\n", + " for level in range(levels): #для каждого уровня а.к.а. выбора лево или право\n", + " index += np.random.choice([-1, 1]) #вычисляем итоговую позицию шарика в конце как сумму сдвижек всех выборов\n", + " data.setdefault(index, 0)# инициализируем \n", + " data[index] += 1\n", + " \n", + "sns.barplot(x=list(data.keys()), y=list(data.values())); #создаём гистограмму" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Z-преобразование\n", + "\n", + "Преобразование полученных данных в стандартную Z-шкалу (Z-scores) со средним значением = 0 и дисперсией = 1. Чтобы привести к такому виду из каждого наблюдения нужно отнять среднее значение и разделить на стандартное отклонение. \n", + "\n", + "$$ Z_{i}=\\frac{x_{i} - \\bar{X}}{sd} $$\n", + "\n", + "Иногда нам необходимо рассчитать z - значение только для отдельно взятого наблюдения, чтоб выяснить насколько далеко оно отклоняется от среднего значения в единицах стандартного отклонения.\n", + "\n", + "### Правило 3х-сигм\n", + "\n", + "\n", + "\n", + "\n", + "### 3.Примеры" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "''' Считается, что значение IQ (уровень интеллекта) у людей имеет нормальное распределение\n", + "со средним значением равным 100 и стандартным отклонением равным 15 (M = 100, sd = 15).\n", + "Какой приблизительно процент людей обладает IQ > 125?\n", + "'''\n", + "\n", + "from scipy import stats\n", + "\n", + "mean = 100\n", + "std = 15\n", + "IQ=120\n", + "# sf - Survival function = (1 - cdf) - Cumulative distribution function\n", + "print(f\"Только у {(stats.norm(mean, std).sf(IQ))*100:.2f}% людей, IQ>{IQ}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Центральная предельная теорема\n", + "\n", + "Гласит, что множество средних выборок из генеральной совокупности (ГС необязательно иметь нормальное распределние) будут иметь нормальное распределение. Причём средняя этого распределения будет близко к средней генеральной совокупности, а стандарное отклонение этого распределение будет называться **стандартной ошибкой среднего** (se).\n", + "\n", + "Зная стандартное отклонение ГС и размер выборки мы можем рассчитать стандартную ошибку среднего.\n", + "\n", + "$$ se = \\frac{\\sigma}{\\sqrt{N}} $$\n", + "\n", + "где N - размер выборки. Если размер выборки достаточно большой (>30) и она является репрезативна, то вместо стандарного отклонения ГС мы можем взять стандарное отклонение выборки.\n", + "\n", + "$$ se = \\frac{sd}{\\sqrt{N}} $$\n", + "\n", + "Стандартная ошибка среднего - это среднеквадратическое отклонение распределения выборочных средних\n", + "### 4.Примеры\n", + "Проверим на практике все эти законы." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "import math\n", + "\n", + "# значения игральной кости\n", + "dice = [1, 2, 3, 4, 5, 6]\n", + "# количество бросков кости\n", + "count = 6\n", + "# размер генеральной совокупности\n", + "sp_size = 100000\n", + "# sp - Statistical population - генеральная совокупность\n", + "sp = pd.Series(dtype=np.int64, index=range(sp_size))\n", + "for i in range(sp_size):\n", + " throws_sum = 0\n", + " for throw in range(count):\n", + " throws_sum += np.random.choice(dice)\n", + " sp[i] = throws_sum\n", + "\n", + "sp.plot.hist(bins=(36-6), xlabel='Сумма костей', ylabel='Частота')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# количество выборок\n", + "samples_count = 10\n", + "# размер выборки\n", + "sample_size = 200\n", + "\n", + "histos = {}\n", + "for sample in range(samples_count):\n", + " histos[f'Выборка №{sample+1}'] = [np.random.choice(sp) for element in range(sample_size)]\n", + "\n", + "samples = pd.DataFrame(histos)\n", + "\n", + "samples.hist(figsize=(16, 10), sharex=True, sharey=True)\n", + "plt.subplots_adjust(hspace = 0.6)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "means = samples.mean()\n", + "print(f'сравним среднию ГС: {sp.mean()}')\n", + "print(f'и среднию средних выборок: {means.mean()}')\n", + "print('их разница:', abs(means.mean() - sp.mean()))\n", + "print('и стандартная ошибка среднего:', means.std())" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# возьмём произвольную выборку \n", + "sample = samples.iloc[0]\n", + "print('sample mean:', sample.mean())\n", + "print('sample SE: ', sample.std()/math.sqrt(sample.size))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### P.S. Важное замечание о ЦПТ номер 2.\n", + "\n", + "Пожалую самый сложный момент - это как мы так взяли и заменили стандартное отклонение генеральной совокупности на выборочное. Ну и что с того, что у нас выборка объемом больше 30 наблюдений, что за магическое число такое? \n", + "\n", + "Все правильно, никакой магии не происходит. И совсем скоро мы в этом окончательно разберемся. Как только пройдем тему t - распределения во втором модуле. Вот тут я подробно расписал, как же нам нужно рассчитывать стандартную ошибку среднего, если мы не знаем стандартное отклонение в генеральной совокупности." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Доверительные интервалы для среднего\n", + "\n", + "Если мы имеем некоторую выборку и ГС, то мы **не можем точно** знать среднюю ГС, зная только среднее выборки. Однако **мы можем сказать, с некоторым процентом уверенности**, в каком интервале лежит средняя ГС. Понятно дело, что для нас лучше, чтобы этот интервал был как можно меньше, как это сделать?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Мы знаем, средняя средних выборок, стремится к средней ГС, также мы знаем, что стандартная ошибка среднего описывает стандартное отклонение распределения средних выборок. Если мы возьмём случайную выборку $X$ и найдём её среднее $\\bar{X}$, а также вычислим стандартную ошибку $se$, то мы можем вычислить доверительный интевал $[\\bar{X} - 1.96*se; \\bar{X} + 1.96*se]$ который описывает среднюю ГС с некотором интервале с 95% доверия.\n", + "\n", + "Загадочное число **1,96** это количество сигм $\\sigma$ в нормальном распределение, необходимые, чтобы охватить **95%** значений в этом распределнии.\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Если мы рассчитали 95% доверительный интервал для среднего значения, это значит:\n", + "\n", + " - Среднее значение в генеральной совокупности точно принадлежит рассчитанному доверительному интервалу.\n", + " - Мы можем быть на 95% уверены, что среднее значение в генеральной совокупности принадлежит рассчитанному доверительному интервалу.\n", + " - Если многократно повторять эксперимент, для каждой выборки рассчитывать свой доверительный интервал, то в 95 % случаев истинное среднее будет находиться внутри доверительного интервала.\n", + " - Среднее значение в генеральной совокупности точно превышает нижнюю границу 95% доверительного интервала.\n", + " - Если многократно повторять эксперимент, то 95 % выборочных средних значений будут принадлежать рассчитанному нами доверительному интервалу.\n", + " \n", + " __Если из лекции усвоить разницу между средним ГС и средним выборки, а так же понять, что доверительный интервал строится для выборки, а не для ГС, то ответы в тесте легко определяются.__\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "'''Вычисление 1.96 c помощью scipy'''\n", + "from scipy import stats\n", + "\n", + "# 95%\n", + "p = 0.95\n", + "# так как у нас двухсторонний интервал, сделаем вычисление\n", + "alpha = (1-p)/2\n", + "# isf - Inverse survival function (inverse of sf) \n", + "print(f'{stats.norm().isf(alpha):.2f} sigma')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "'''Рассчитайте 99% доверительный интервал для следующего примера: \n", + "среднее = 10, стандартное отклонение = 5, размер выборки = 100\n", + "'''\n", + "from numpy import sqrt\n", + "from scipy import stats\n", + "\n", + "p = 0.99\n", + "mean = 10\n", + "std = 5\n", + "n = 100\n", + "\n", + "se = std/sqrt(n)\n", + "alpha = (1-p)/2\n", + "sigma = stats.norm().isf(alpha)\n", + "сonfidence_interval = mean - sigma*se, mean + sigma*se\n", + "print('[%.2f; %.2f]' % сonfidence_interval)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Идея статистического вывода\n", + "### Статистическая проверка гипотез\n", + "\n", + "\n", + "### p-уровень значимости\n", + "\n", + "p-уровень значимости - это вероятность получить такие или более выраженные различия при условии, что в генеральной совокупности никаких различий на самом деле нет.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Часть 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## T-распределение\n", + "\n", + "Распределение Стьюдента по сути представляет собой сумму нескольких нормально распределенных случайных величин. Чем больше величин, тем больше верятность, что их сумма будет иметь нормальное распределение. Таким образом, количество суммируемых величин определяет важнейший параметр формы данного распредения - число степеней свободы." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "'''График снизу показывает, как меняется форма распределения при увеличение количества степеней свободы.\n", + "А также показывает приближение t-распредееления к нормальному по мере увеличения степеней свободы.'''\n", + "from scipy.stats import t, norm\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "df1, df2, df3 = 1, 3, 3\n", + "\n", + "x = np.linspace(-5, 5, 100)\n", + "y1, y2, y3 = t.pdf(x, df=df1), t.pdf(x, df=df2), t.pdf(x, df=df3)\n", + "y4 = norm.pdf(x)\n", + "lable1, lable2, lable3 = 'df = '+str(df1), 'df = '+str(df2), 'd3 = '+str(df3)\n", + "plt.title('графики t-распредления с разными степенями свободы')\n", + "plt.plot(x, y1)\n", + "plt.plot(x, y2)\n", + "plt.plot(x, y3)\n", + "plt.plot(x, y4, 'r:')\n", + "plt.legend((lable1, lable2, lable3, 'norm'))\n", + "plt.show()\n", + "norm_p = stats.norm(0, 1).sf(2)*100\n", + "t_p = stats.t(df3).sf(2)*100\n", + "print(f\"Norm. P(x>2) = {norm_p:.2f}%\")\n", + "print(f\"t. P(x>2) = {t_p:.2f}%\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "График плотности распределения Стьюдента, как и нормального распределения, является симметричным и имеет вид колокола, но с более «тяжёлыми» хвостами." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Подробно про нормальное и t-распредление\n", + "\n", + "В видео лекциях говорилось, что мы используем t-распределение в ситуации небольшого объема выборки. Необходимо более подробно пояснить, зачем это нужно.\n", + "\n", + "Вернемся к предельной центральной теореме, мы уже узнали, что если некий признак в генеральной совокупности распределен **нормально** со средним $\\mu$ и стандартным отклонением $\\sigma$, и мы будем многократно извлекать выборки одинакового размера n, и для каждой выборки рассчитывать, как далеко выборочное среднее $\\bar{X}$ ˉ\n", + " отклонилось от среднего в генеральной совокупности в единицах стандартной ошибки среднего:\n", + " \n", + "\n", + "$$\\large z = \\frac{\\bar{X} - \\mu}{\\frac{\\sigma}{\\sqrt{n}}}$$\n", + "\n", + "то эта величина z будет иметь стандартное нормальное распределение со средним равным нулю и стандартным отклонением равным единице.\n", + "\n", + "Обратите внимание, что для расчета стандартной ошибки мы используем именно стандартное отклонение в генеральной совокупности - $\\sigma$. Ранее мы уже обсуждали, что на практике $\\sigma$ нам практически никогда не известна, и для расчета стандартной ошибки мы используем выборочное стандартное отклонение.\n", + "\n", + "Так вот, строго говоря в таком случае распределение отклонения выборочного среднего и среднего в генеральной совокупности, деленного на стандартную ошибку, теперь будет описываться именно при помощи t - распределения.\n", + "\n", + "$$\\large t = \\frac{\\bar{X} - \\mu}{\\frac{sd}{\\sqrt{n}}}$$\n", + "\n", + "\n", + "таким образом, в случае неизвестной $\\sigma$ мы **всегда будем иметь дело с t-распределением**. На этом этапе вы должны с негодованием спросить меня, почему же мы применяли z-критерий в первом модуле курса, для проверки гипотез, используя выборочное стандартное отклонение?\n", + "\n", + "Мы уже знаем, что при довольно большом объеме выборки (обычно в учебниках приводится правило, n > 30) t-распределение совсем близко подбирается к нормальному распределению:\n", + "\n", + "Поэтому иногда, для простоты расчетов говорится, что если n > 30, то мы будем использовать свойства нормального распределения для наших целей. Строго говоря, это конечно неправильный подход, который часто критикуют. В до компьютерную эпоху этому было некоторое объяснение, чтобы не рассчитывать для каждого n больше 30 соответствующее критическое значение t - распределения, статистики как бы округляли результат и использовали нормальное распределение для этих целей. Сегодня, конечно, с этим больше никаких проблем нет, и все статистические программы, разумеется, без труда рассчитают все необходимые показатели для t - распределения с любым числом степеней свободы. Действительно при выборках очень большого объема t - распределение практически не будет отличаться от нормального, однако, хоть и очень малые но различия все равно будут.\n", + "\n", + "Поэтому, правильнее будет сказать, что мы используем t - распределение не потому что у нас маленькие выборки, а потому что мы не знаем стандартное отклонение в генеральной совокупности. Поэтому в дальнейшем мы всегда будем использовать t - распределение для проверки гипотез, если нам неизвестно стандартное отклонение в генеральной совокупности, необходимое для расчета стандартной ошибки, даже если объем выборки больше 30.\n", + "\n", + "### 5.Примеры" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "'''На выборке в 15 наблюдений при помощи одновыборочного t-теста\n", + "проверяется нулевая гипотеза: μ=10 \n", + "и рассчитанное t-значение равняется -2 (t = -2), то p-уровень значимости (двусторонний) равен:\n", + "'''\n", + "from scipy import stats\n", + "\n", + "t = -2\n", + "n = 15\n", + "df = n - 1\n", + "\n", + "p = 2 * stats.t.sf(abs(t), df)\n", + "print(f'p = {p:.3f}')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Сравнение двух средних. t-критерий Стьюдента\n", + "\n", + "t-критерий Стьюдента — общее название для статистических тестов, в которых статистика критерия имеет распределение Стьюдента. Наиболее часто t-критерии применяются для проверки равенства средних значений в двух выборках. Нулевая гипотеза предполагает, что средние равны (отрицание этого предположения называют гипотезой сдвига). Для применения данного критерия необходимо, чтобы исходные данные имели нормальное распределение. \n", + "\n", + "$$ t = \\frac{\\bar{X_1} - \\bar{X_2}}{se}$$\n", + "\n", + "$$ se = \\sqrt{\\frac{sd_1^2}{n_1} + \\frac{sd_2^2}{n_2}} $$\n", + "\n", + "Откуда берётся такая формула $se$?:\n", + "\n", + "$$ (se_1)^2 = (\\frac{sd_1}{\\sqrt{n_1}})^2 = \\frac{sd_1^2}{n_1} $$\n", + " \n", + "То есть:\n", + "\n", + "$$ se = \\sqrt{\\frac{sd_1^2}{n_1} + \\frac{sd_2^2}{n_2}} = \\sqrt{se_1^2 + se_2^2} $$\n", + "\n", + "причем ответ на вопрос, почему верно это равенство, кроется в свойстве дисперсии: дисперсия суммы независимых случайных величин равна сумме их дисперсий. а отклонение - это корень из дисперсии. отсюда ваша последняя формула" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Примеры применения t-критерий Стьюдента\n", + "**Пример 1.** Первая выборка — это пациенты, которых лечили препаратом А. Вторая выборка — пациенты, которых лечили препаратом Б. Значения в выборках — это некоторая характеристика эффективности лечения (уровень метаболита в крови, температура через три дня после начала лечения, срок выздоровления, число койко-дней, и т.д.) Требуется выяснить, имеется ли значимое различие эффективности препаратов А и Б, или различия являются чисто случайными и объясняются «естественной» дисперсией выбранной характеристики.\n", + "\n", + "**Пример 2.** Первая выборка — это значения некоторой характеристики состояния пациентов, записанные до лечения. Вторая выборка — это значения той же характеристики состояния тех же пациентов, записанные после лечения. Объёмы обеих выборок обязаны совпадать; более того, порядок элементов (в данном случае пациентов) в выборках также обязан совпадать. Такие выборки называются связными. Требуется выяснить, имеется ли значимое отличие в состоянии пациентов до и после лечения, или различия чисто случайны.\n", + "\n", + "**Пример 3.** Первая выборка — это поля, обработанные агротехническим методом А. Вторая выборка — поля, обработанные агротехническим методом Б. Значения в выборках — это урожайность. Требуется выяснить, является ли один из методов эффективнее другого, или различия урожайности обусловлены случайными факторами.\n", + "\n", + "**Пример 4.** Первая выборка — это дни, когда в супермаркете проходила промо-акция типа А (красные ценники со скидкой). Вторая выборка — дни промо-акции типа Б (каждая пятая пачка бесплатно). Значения в выборках — это показатель эффективности промо-акции (объём продаж, либо выручка в рублях). Требуется выяснить, какой из типов промо-акции более эффективен.\n", + "\n", + "### 6. Примеры" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import pandas as pd\n", + "from scipy.stats import t\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "array1 = np.array([84.7, 105.0, 98.9, 97.9, 108.7, 81.3, 99.4, 89.4, 93.0,\n", + " 119.3, 99.2, 99.4, 97.1, 112.4, 99.8, 94.7, 114.0, 95.1, 115.5, 111.5])\n", + "array2 = np.array([57.2, 68.6, 104.4, 95.1, 89.9, 70.8, 83.5, 60.1, 75.7,\n", + " 102.0, 69.0, 79.6, 68.9, 98.6, 76.0, 74.8, 56.0, 55.6, 69.4, 59.5])\n", + "\n", + "# считаем количество элементов, среднее, стандартное отклонение и стандартную ошибку\n", + "df = pd.DataFrame({'Выборка №1':array1, 'Выборка №2':array2}).agg(['mean','std','count','sem']).transpose()\n", + "df.columns = ['Mx','SD','N','SE']\n", + "\n", + "# рассчитываем 95% интервал отклонения среднего\n", + "p = 0.95\n", + "K = t.ppf((1 + p)/2, df['Mx']-1)\n", + "df['interval'] = K * df['SE']\n", + "\n", + "df" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#строим графики, boxplot из изначальных данных array1, array2, доверительные интервалы из датафрейма df\n", + "fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(14, 9))\n", + "\n", + "# график boxplot\n", + "bplot1 = ax1.boxplot([array1, array2],\n", + " vert=True, # создаем вертикальные боксы\n", + " patch_artist=True, # для красоты заполним цветом боксы квантилей\n", + " labels=['Выборка №1', 'Выборка №2']) # используется для задания значений выборок в случае с boxplot\n", + "\n", + "# график доверительных интервалов\n", + "bplot2 = ax2.errorbar(x=df.index, y=df['Mx'], yerr=df['interval'],\\\n", + " color=\"black\", capsize=3, marker=\"s\", markersize=4, mfc=\"red\", mec=\"black\", fmt ='o')\n", + "\n", + "# раскрасим boxplot \n", + "colors = ['pink', 'lightgreen']\n", + "for patch, color in zip(bplot1['boxes'], colors):\n", + " patch.set_facecolor(color)\n", + " \n", + "# добавим общие для каждого из графиков данные\n", + "for ax in [ax1, ax2]:\n", + " ax.yaxis.grid(True)\n", + " ax.set_title('Температура плавления ДНК двух типов')\n", + " ax.set_xlabel('Сравнение двух выборок')\n", + " ax.set_ylabel('Температура F')\n", + " \n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Задача \n", + "\n", + "Рассчитайте доверительный интервал основываясь на знании t - распределения для среднего значения температуры плавления ДНК у первого вида:\n", + "\n", + "$$ \\bar{X}=89,9\\quad sd=11,3\\quad n=20 $$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy import stats\n", + "from math import sqrt\n", + "\n", + "mean = 89.9\n", + "sd = 11.3\n", + "n = 20\n", + "# степень свободы\n", + "df = n - 1\n", + "# 95% доверительный интервал\n", + "p = 0.95\n", + "alpha = 1-p\n", + "# стандартная ошибка\n", + "se = sd/sqrt(n)\n", + "\n", + "# ppf - Percent point function\n", + "# делим на два, так как по умолчанию функция считает для одного конца, а нам надо для двух\n", + "t_value = stats.t(df).ppf(1-(alpha/2))\n", + "\n", + "# доверительный интервал \n", + "сonfidence_interval = (mean-t_value*se, mean+t_value*se)\n", + "print('[%.2f; %.2f]' % сonfidence_interval)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Первые премии Оскар за лучшую мужскую и женскую роль были вручены в 1929. Данные гистограммы демонстрируют распределение возраста победителей с 1929 по 2014 год (100 мужчин, 100 женщин). Используя t - критерий проверьте, можно ли считать наблюдаемые различия в возрасте между лучшими актрисами и актерами статистически достоверными.\n", + "\n", + "Средний возраст мужчин равен 45, sd = 9.\n", + "\n", + "Средний возраст женщин равен 34, sd = 10.\n", + "\n", + "" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.stats import t\n", + "from numpy import sqrt\n", + "\n", + "mean_m, mean_f = 45, 34\n", + "sd_m, sd_f = 9, 10\n", + "N = 100\n", + "\n", + "se = sqrt((sd_m ** 2)/N + (sd_f ** 2)/N)\n", + "t_value = (mean_m - mean_f)/se\n", + "\n", + "p = t.sf(t_value, N-2)\n", + "print(f'p={p}')\n", + "if p >= 0.05:\n", + " print('Мы НЕ можем отклонить нулевую гипотезу')\n", + "else:\n", + " print('Мы можем отклонить нулевую гипотезу')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Проверка распределения на нормальность\n", + "\n", + "### QQ-plot\n", + "\n", + "### Примеры" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np \n", + "import scipy.stats as stats\n", + "import matplotlib.pyplot as plt\n", + "\n", + "plt.rcParams['figure.figsize'] = [12, 6]\n", + "\n", + "mu, sigma = 10, 4\n", + "n = 1000 # с ростом числа точек в распределении qq-plot стремится к прямой\n", + "sequence = np.random.normal(mu, sigma, n)\n", + "\n", + "\n", + "fig, (ax1, ax2) = plt.subplots(1, 2)\n", + "fig.suptitle('QQ Plot', fontsize=18)\n", + "\n", + "# Q-Q Plot graph\n", + "stats.probplot(sequence, dist=\"norm\", plot=ax1)\n", + "ax1.set_title(\"Normal Q-Q Plot\")\n", + "\n", + "# normal distribution histogram + distribution\n", + "count, bins, _ = ax2.hist(sequence, 25, density=True)\n", + "p_x = 1/(sigma * np.sqrt(2 * np.pi)) * np.exp( - (bins - mu)**2 / (2 * sigma**2) )\n", + "ax2.plot(bins, p_x, color='r')\n", + " \n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Однофакторный дисперсионный анализ\n", + "\n", + "Рассмотренный ранее **t-критерий Стьюдента** (равно как и его непараметрические аналоги) предназначен для сравнения исключительно **двух совокупностей**. В таком случае мы можем применять однофакторный дисперсионный анализ. Та переменная, которая будет разделять наших испытуемых или наблюдения на группы (номинативная переменная с нескольким градациями) называется **независимой переменной**. А та количественная переменная, по степени выраженности которой мы сравниваем группы, называется **зависимая переменная**. \n", + "\n", + "\n", + "$$ SS_{total} = \\sum_{j=1}^{p}{\\sum_{i=1}^{n_j}{(x_{ij} - \\bar{x})^2}} = SS_{between} + SS_{within} $$\n", + "$$ SS_{between} = \\sum_{j=1}^{p}{n_j{(\\bar{x}_j - \\bar{x})^2}} $$\n", + "$$ SS_{within} = \\sum_{j=1}^{p}{\\sum_{i=1}^{n_j}{(x_{ij} - \\bar{x}_j)^2}} $$\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy import stats\n", + "import pandas as pd\n", + "\n", + "# Выборки которые надо сравнить\n", + "data = pd.DataFrame({\n", + " 'a': [3, 1, 2],\n", + " 'b': [5, 3, 4],\n", + " 'c': [7, 6, 5]\n", + " })\n", + "data.boxplot()\n", + "print('Нулевая гипотеза:', '='.join(data))\n", + "print('Альтернативная гипотеза:', f'!({\"=\".join(data)})')\n", + "# общая средняя\n", + "grand_mean = data.values.flatten().mean()\n", + "# отклонение групповых средний от общей средней\n", + "ssb = sum(data[group].size * (group_mean - grand_mean)**2 for group, group_mean in data.mean().items())\n", + "# отклонения значений в внутри группы от средней группы\n", + "ssw = sum(sum((x - group_mean)**2 for x in data[group]) for group, group_mean in data.mean().items())\n", + "\n", + "groups = data.shape[1]\n", + "dfb = groups - 1\n", + "dfw = data.size - groups\n", + "# межгрупповой средний квадрат \n", + "mssb = ssb/dfb\n", + "# внутригрупповой средний квадрат\n", + "mssw = ssw/dfw\n", + "\n", + "f_value = mssb/mssw\n", + "\n", + "p = stats.f.sf(f_value, dfb, dfw)\n", + "print('Результат:')\n", + "if p < 0.05:\n", + " print('отклоняем нулевую гипотезу')\n", + "else:\n", + " print('НЕ отклоняем нулевую гипотезу')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Множественные сравнения в ANOVA\n", + "\n", + "В отличие от t-критерия, позволяет сравнивать средние значения трёх и более групп. Разработан Р. Фишером для анализа результатов экспериментальных исследований. \n", + "\n", + "В литературе также встречается обозначение **ANOVA** (от англ. **AN**alysis **O**f **VA**riance) - дисперсионный анализ\n", + "\n", + "**Почему мы не можем применить t-критерий для более двух выборок применяя его попарно к каждой выбрке?**\n", + "\n", + "Чтобы выяснить это, сделаем эксперемент." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from numpy import random\n", + "import matplotlib.pyplot as plt\n", + "from scipy.stats import t\n", + "\n", + "\n", + "def pair_t(samples, alpha) -> np.bool:\n", + " '''\n", + " Парный t-критерий, если все переданные выборки\n", + " попарно взяты из одной ГС, возвращает True\n", + " '''\n", + " n_samples = samples.shape[0] \n", + " n_combinations = n_samples*(n_samples - 1)//2 # число комбинациий для сранения по t-критерию, см https://ru.wikipedia.org/wiki/Сочетание \n", + " result = np.zeros(n_combinations, dtype=bool)\n", + " k = 0\n", + " for i in range(n_samples):\n", + " for j in range(i+1, n_samples):\n", + " N = samples[i].size\n", + " std_err = np.sqrt((samples[i].std()**2)/N + (samples[j].std()**2)/N)\n", + " t_value = (samples[i].mean() - samples[j].mean())/std_err\n", + " p = 2*t.sf(x=t_value, df=2*N-2) # умножаем на два, так как смотрим на два хвоста распределения \n", + " result[k] = (p >= alpha)\n", + " k += 1\n", + " return np.all(result)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def pair_t_test(repeat, n_samples, sample_size, ax, alpha=0.05):\n", + " '''\n", + " функция показывает, сколько у нас будет ложных результатов, при парном сравнение множества выборок\n", + " с помощью t-критерия\n", + " \n", + " repeat, n_samples, sample_size = количество повторов, количество выборок в каждом повторе, размер выборки\n", + " ax - для рисования\n", + " '''\n", + " result = np.zeros(repeat, dtype=bool)\n", + " for i in range(repeat):\n", + " samples = random.randn(n_samples, sample_size)\n", + " result[i] = pair_t(samples, alpha)\n", + " \n", + " unique, counts = np.unique(result, return_counts=True)\n", + " percentage = counts/result.size\n", + " ax.pie(percentage, normalize=False, labels=unique, autopct='%.0f%%')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, axs = plt.subplots(ncols=4, figsize=(20, 5))\n", + "n_samples = [2, 4, 8, 16]\n", + "fig.suptitle('Процент ошибок (False) при попарном сравнение выборок t-критерием')\n", + "\n", + "for n, ax in zip(n_samples, axs):\n", + " pair_t_test(repeat=1000, n_samples=n, sample_size=100, ax=ax)\n", + " ax.set_title(f'{n} samples')\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Как мы и ожидаем, степень ошибки примерно должна быть равна **5%**, при сравнении **двух выборок** из одной ГС с помощью t-критерия с p-уровнем значимости **95%**. \n", + "\n", + "Если мы возмём больше выборок то процент ошибок будет возрастать с каждым увеличением числа выборок примерно как отношение сочетаний нового числа выборок к предыдущему, что совершенно неприемлемо.\n", + "\n", + "Причина такого возрастания ошибки в расмотрении всё большего числа комбинаций. Так как наше условие проверки множества выборок требует различия хотя бы пары, вероятность того, что это произойдёт при увеличении числа сравниваемых выборок стремится к единице.\n", + "\n", + "Решение этой проблемы - поправки на множественное сравнение для p-уровня значимости. А самая популярная такая поправка - поправка Бонферрони." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Поправка Бонферрони\n", + "\n", + "Поправка Бонферрони весьма интуитивна. Если вероятность ошибки растёт пропорционально числу сочетаний рассматриваемых в эксперименте выборок - $C^2_n$, то есть числу проверяемых гипотез, то нужно ужесточить критерий $\\alpha$ так же пропорционально этому числу: $\\alpha' = \\alpha / C^2_n$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# применим поправку Бонферрони\n", + "fig, axs = plt.subplots(ncols=4, figsize=(20, 4))\n", + "n_samples = [2, 4, 8, 16]\n", + "fig.suptitle('Процент ошибок при попарном сравнение выборок t-критерием с корректировкой уровня значимости')\n", + "\n", + "for n, ax in zip(n_samples, axs):\n", + " alpha = 0.05/((n*(n-1))/2) # ужесточили критерий\n", + " pair_t_test(1000, n, 100, ax, alpha)\n", + " ax.set_title(f'{n} samples')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "С новым показателем $\\alpha$ процент ошибки стал правтикчески одинаковым вне зависимости от числа рассматриваемых гипотез - это успех!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Однако в данном случае эта будет сверх-консервативная корректировавка, которая имеет меньше вероятность найти реальные значения. По сути мы **уменьшаем шанс получить ошибку I рода, но увеличиваем шанс на ошибку II рода**. То есть мы уничтожаем очень много \"полезных\" результатов в эксперименте.\n", + "\n", + "\n", + "\n", + "Так не применять какую-то корректировку для множественного сравнения невозможно, но сильно увеличивать ошибку II рода не хочется, были разработаны более подходящие способы поправки, чем поправка Бонферрони. Пример более продвинутого метода - **критерий Тьюки**." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Критерий Тьюки" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Многофакторный ANOVA\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Двухфакторный дисперсионный анализ\n", + "\n", + "В случе двухфакторного анализа (он же Two-way analysis of variance) мы можем учитывать взаимосвязь нашей зависимой переменной не с одним фактором (одной номининативной перменной), а с двумя.\n", + "\n", + "Основная идея двухфаткорного дисперсионного анализа сводится к тому, что теперь у нас общая изменчивость $SS_{total}$ складывается из следующих четырёх компонент:\n", + "\n", + "$ SS_{total} = SSW + SSB_A + SSB_B + SSB_{A}*SSB_{B}, $ \n", + "\n", + "где $SSW$ - это внутригрупповая изменчивость, $SSB_A$ - изменчивость, обусловленная влиянием первого фактора, $SSB_B$ - изменчивость, обусловленная влиянием второго фактора, $SSB_{A}*SSB_{B}$ - изменчивость, обусловленная взаимодействием двух факторов." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Пример\n", + "Атеросклероз довольно опасное заболевание причина ишемической болезни сердца и инсультов. Анализ экспрессии генов лейкоцитов позволяет предсказать вероятность развития данного заболевания. В эксперименте исследовался уровень экспрессии в зависимости от возраста пациентов и дозировки лекарства аторвастатина. Понятно, что в данном исследовании экпрессия (expr) это зависимая переменная, а два фактора - возраст (age) и дозировка лекарства (dose).\n", + "\n", + "Рассмотрим две гипотезы $H_0$: \n", + "1. Отсутвует статистически значимое влияние возраста на экспрессию гена.\n", + "2. Отсутвует статистически значимое влияние дозировки лекраства на экспрессию гена.\n", + "\n", + "Для анализа можно разделить выборку на 4 подгруппы - молодые с высокой дозировкой, молодые с низкой дозировкой, пожилые с высокой дозировкой, и пожилые с низкой дозировкой." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# построим график измерений\n", + "import pandas as pd\n", + "import seaborn as sns\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "ather_data = pd.read_csv('../../data/atherosclerosis.csv') # считываем файл с данными\n", + "sns.set_theme(rc={'figure.figsize':(15, 10)}) # задаем размеры выводимого графика\n", + "pplot = sns.pointplot(x='dose', y='expr', hue='age', palette='bright', dodge=0.1, capsize=.1, data=ather_data)# строим график с помощью seaborn\n", + "\n", + "# меняем названия титула, оси х и оси у\n", + "plt.title('Экспрессия гена в зависимости от дозировки и возраста пациентов', fontsize=25)\n", + "plt.xlabel('Дозировка', fontsize=20)\n", + "plt.ylabel('Уровень экспрессии', fontsize=20)\n", + "\n", + "bars = ('низкая', 'высокая')\n", + "x_pos = np.arange(len(bars))\n", + "plt.xticks(x_pos, bars, fontsize=15) # меняем названия отложенных по оси х значений\n", + "\n", + "# меняем \"Легенду\", ту, что в верхнем правом углу\n", + "leg_handles = pplot.get_legend_handles_labels()[0]\n", + "pplot.legend(leg_handles, ['молодые', 'пожилые'], title='Возраст', title_fontsize=20, fontsize=15)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# вывод результатов дисперсионного анализа\n", + "import pandas as pd\n", + "import scipy.stats as stats\n", + "\n", + "alpha = 0.05\n", + "\n", + "df = pd.read_csv('../../data/atherosclerosis.csv')\n", + "print('Dataframe sample:\\n', df.head(10), '\\n')\n", + "print('Dataframe types:\\n', df.dtypes, '\\n')\n", + "print('Dataframe stats:\\n', df.describe(), '\\n')\n", + "\n", + "#разделим выборку на подгруппы\n", + "df_young_high = df[(df['age'] == 1) & (df['dose'] == 'D1')]['expr']\n", + "df_young_low = df[(df['age'] == 1) & (df['dose'] == 'D2')]['expr']\n", + "df_old_high = df[(df['age'] == 2) & (df['dose'] == 'D1')]['expr']\n", + "df_old_low = df[(df['age'] == 2) & (df['dose'] == 'D2')]['expr']\n", + "\n", + "# посчитаем число наблюдений\n", + "N = df['expr'].count()\n", + "N_young_high = df_young_high.count()\n", + "N_young_low = df_young_low.count()\n", + "N_old_high = df_old_high.count()\n", + "N_old_low = df_old_low.count()\n", + "\n", + "# посчтиаем средние значения\n", + "Mx = df['expr'].mean()\n", + "Mx_young_high = df_young_high.mean()\n", + "Mx_young_low = df_young_low.mean()\n", + "Mx_old_high = df_old_high.mean()\n", + "Mx_old_low = df_old_low.mean()\n", + "Mx_young = (N_young_high*Mx_young_high + N_young_low*Mx_young_low)/(N_young_high + N_young_low)\n", + "Mx_old = (N_old_high*Mx_old_high + N_old_low*Mx_old_low)/(N_old_high + N_old_low)\n", + "Mx_high = (N_young_high*Mx_young_high + N_old_high*Mx_old_high)/(N_young_high + N_old_high)\n", + "Mx_low = (N_young_low*Mx_young_low + N_old_low*Mx_old_low)/(N_young_low + N_old_low)\n", + "\n", + "# посчитаем стандартные отлонения среднего\n", + "SD = df['expr'].std()\n", + "SD_young_high = df_young_high.std()\n", + "SD_young_low = df_young_low.std()\n", + "SD_old_high = df_old_high.std()\n", + "SD_old_low = df_old_low.std()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Характеристики исследумых подгрупп:\n", + "| Возраст | Дозировка | N | Mx | SD | \n", + "| ------- | --------- | -- | ----- | --- | \n", + "| молодые | высокая | 16 | 104,8 | 5,8 | \n", + "| молодые | низкая | 16 | 105,5 | 4,4 | \n", + "| пожилые | высокая | 16 | 101 | 5,1 | \n", + "| пожилые | низкая | 16 | 102,3 | 5,1 | \n", + "\n", + "N - число элементов, Mx - математическое ожидание, SD - стандратное отклонение среднего" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# посчитаем суммы квадратов\n", + "SS_age = ((Mx - Mx_young)**2)*(N_young_high + N_young_low) + ((Mx - Mx_old)**2)*(N_old_high + N_old_low) # sum of squares for age factor\n", + "print(f'Сумма квадратов по возрасту: {round(SS_age,1)}')\n", + " \n", + "SS_dose = ((Mx - Mx_high)**2)*(N_young_high + N_old_high) + ((Mx - Mx_low)**2)*(N_young_low + N_old_low) # sum of squares for dose factor\n", + "print(f'Сумма квадратов по дозе: {round(SS_dose,1)}')\n", + "\n", + "SS_within = ((df_young_high - Mx_young_high)**2).sum() + ((df_young_low - Mx_young_low)**2).sum() + ((df_old_high - Mx_old_high)**2).sum() + ((df_old_low - Mx_old_low)**2).sum()\n", + "print(f'Сумма квадратов внутри групп: {round(SS_within,1)}')\n", + "\n", + "SS = ((df['expr'] - Mx)**2).sum()\n", + "print(f'Полная сумма квадратов: {round(SS,1)}')\n", + "\n", + "SS_age_dose = SS - SS_within - SS_age - SS_dose\n", + "print(f'Сумма квадратов взаимодействия факторов: {round(SS_age_dose,1)}')\n", + "\n", + "# рассчитаем степени свободы\n", + "Df_age = 2 - 1\n", + "Df_dose = 2 - 1\n", + "Df_age_dose = Df_age*Df_dose\n", + "Df_within = N - 4\n", + "Df = Df_within + Df_age + Df_dose + Df_age_dose\n", + "\n", + "# рассчитаем средние квадраты\n", + "MS_within = SS_within / Df_within\n", + "MS_age = SS_age / Df_age\n", + "MS_dose = SS_dose / Df_dose\n", + "MS = SS / Df\n", + "\n", + "print(f'Среднее квадратов по возрасту: {round(MS_age,2)}')\n", + "print(f'Среднее квадратов по дозе: {round(MS_dose,2)}')\n", + "\n", + "# рассчитаем F-score\n", + "Fs_age = MS_age / MS_within\n", + "Fs_dose = MS_dose / MS_within\n", + "\n", + "print(f'F-score по возрасту: {round(Fs_age,2)}')\n", + "print(f'F-score по дозе: {round(Fs_dose,2)}')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Результаты дисперсионного анализа:\n", + "| | Df | Sum Sq | Mean Sq | F value | Pr(>F) | \n", + "| ---- | -- | ------ | ------- | ------- | ------ |\n", + "| Age | 1 | 197,5 | 197,45 | 7.45* | 0,008 |\n", + "| Dose | 1 | 16,9 | 16,91 | 0,64 | 0,42 | \n", + "| Residuals | 61 | 1591,2 | 26,08 | | | \n", + "\n", + "---\n", + "\\* В оригинале, на слайдах лекций бьло указано число 7,57 для F-значения возраста, расчёт не подтверждает это значение, оно было исправлено как опечатка" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print('Найдём площадь под графиком соответсвующего F-распределения для каждого фактора:\\n')\n", + "\n", + "print(f'Для возраста: F({Df_age},{Df_within}) = {round(Fs_age,2)}, p < 0.05')\n", + "PrF_age = 1 - stats.f.cdf(Fs_age, Df_age, Df_within)\n", + "print(f'Следовательно веротяность превышения этой величины: Pr(>F) = {round(PrF_age,3)}')\n", + "if PrF_age < alpha:\n", + " print('Отбрасываем 1-ую нулевую гипотезу, возраст влияет на экспрессию гена\\n')\n", + "else: \n", + " print('Принимаем 1-ую нулевую гипотезу, возраст не влияет на экспрессию гена\\n')\n", + " \n", + "print(f'Для дозы: F({Df_dose},{Df_within}) = {round(Fs_dose,2)}, p < 0.05')\n", + "PrF_dose = 1 - stats.f.cdf(Fs_dose, Df_dose, Df_within)\n", + "print(f'Следовательно веротяность превышения этой величины: Pr(>F) = {round(PrF_dose,3)}')\n", + "if PrF_dose < alpha:\n", + " print('Отбрасываем 2-ую нулевую гипотезу, доза лекраства влияет на экспрессию гена\\n')\n", + "else: \n", + " print('Принимаем 2-ую нулевую гипотезу, доза лекраства не влияет на экспрессию гена\\n')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Примечение. \n", + "# Здесь ANOVA был выполнен по шагам для целей обучения, однако он, конечно уже давно был автоматизирован.\n", + "# Например, с помощью python модуля statsmodels подобный анализ можно было бы сделать в две строки кода." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Взаимодействие факторов в ANOVA\n", + "\n", + "Возможна ситуация, когда каждый из факторов по отдельности не влияет значимо на наши данные, однако факторы совместно - влияют.\n", + "\n", + "#### Пример\n", + "\n", + "Исследователей интересовало влияние инъекции некоторого гормона на показатель концентрации кальция в плазме крови у птиц с учетом их пола. В таблице представлены данные экспериментальной и контрольной группы.\n", + "\n", + "Рассмотрим три гипотезы $H_0$: \n", + "1. Отсутвует статистически значимое влияние инъекции некоторого гормона на концентрации кальция в плазме крови.\n", + "2. Отсутвует статистически значимое влияние пола птицы на концентрации кальция в плазме крови.\n", + "3. Отсутвует статистически значимое влияние взаимодействия инъекции некоторого гормона и пола птицы на концентрации кальция в плазме крови.\n", + "\n", + "Для анализа можно разделить выборку на 4 подгруппы - нет инъекции и пол птицы мужской, нет инъекции пол птицы женский, сделана инъекция пол птицы мужской, сделана инъекция и пол птицы женский." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# построим график измерений\n", + "import pandas as pd\n", + "import seaborn as sns\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "birds_data = pd.read_csv('../../data/birds.csv') # считываем файл с данными\n", + "sns.set_theme(rc={'figure.figsize':(15, 10)}) # задаем размеры выводимого графика\n", + "pplot = sns.pointplot(x='hormone', y='var4', hue='sex', dodge=0.1, capsize=.1, data=birds_data)# строим график с помощью seaborn\n", + "\n", + "# меняем названия титула, оси х и оси у\n", + "plt.title('Исследование концентрации калия в плазме крови птиц', fontsize=25)\n", + "plt.xlabel('Инъекция гормона', fontsize=20)\n", + "plt.ylabel('Концентрация', fontsize=20)\n", + "\n", + "bars = ('Введена', 'Не введена')\n", + "x_pos = np.arange(len(bars))\n", + "plt.xticks(x_pos, bars, fontsize=15) # меняем названия отложенных по оси х значений\n", + "\n", + "# меняем \"Легенду\", ту, что в верхнем правом углу\n", + "leg_handles = pplot.get_legend_handles_labels()[0]\n", + "pplot.legend(leg_handles, ['Мужской', 'Женский'], title='Пол птиц', title_fontsize=20, fontsize=15)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# вывод результатов дисперсионного анализа\n", + "import pandas as pd\n", + "import scipy.stats as stats\n", + "\n", + "alpha = 0.05\n", + "\n", + "df = pd.read_csv('../../data/birds.csv')\n", + "print('Dataframe sample:\\n', df.head(10), '\\n')\n", + "print('Dataframe types:\\n', df.dtypes, '\\n')\n", + "print('Dataframe stats:\\n', df.describe(), '\\n')\n", + "\n", + "#разделим выборку на подгруппы\n", + "df_nhrm_male = df[(df['hormone'] == 0) & (df['sex'] == 0)]['var4']\n", + "df_nhrm_female = df[(df['hormone'] == 0) & (df['sex'] == 1)]['var4']\n", + "df_yhrm_male = df[(df['hormone'] == 1) & (df['sex'] == 0)]['var4']\n", + "df_yhrm_female = df[(df['hormone'] == 1) & (df['sex'] == 1)]['var4']\n", + "\n", + "# посчитаем число наблюдений\n", + "N = df['var4'].count()\n", + "N_nhrm_male = df_nhrm_male.count()\n", + "N_nhrm_female = df_nhrm_female.count()\n", + "N_yhrm_male = df_yhrm_male.count()\n", + "N_yhrm_female = df_yhrm_female.count()\n", + "\n", + "# посчтиаем средние значения\n", + "Mx = df['var4'].mean()\n", + "Mx_nhrm_male = df_nhrm_male.mean()\n", + "Mx_nhrm_female = df_nhrm_female.mean()\n", + "Mx_yhrm_male = df_yhrm_male.mean()\n", + "Mx_yhrm_female = df_yhrm_female.mean()\n", + "Mx_nhrm = (N_nhrm_male*Mx_nhrm_male + N_nhrm_female*Mx_nhrm_female)/(N_nhrm_male + N_nhrm_female)\n", + "Mx_yhrm = (N_yhrm_male*Mx_yhrm_male + N_yhrm_female*Mx_yhrm_female)/(N_yhrm_male + N_yhrm_female)\n", + "Mx_male = (N_nhrm_male*Mx_nhrm_male + N_yhrm_male*Mx_yhrm_male)/(N_nhrm_male + N_yhrm_male)\n", + "Mx_female = (N_nhrm_female*Mx_nhrm_female + N_yhrm_female*Mx_yhrm_female)/(N_nhrm_female + N_yhrm_female)\n", + "\n", + "# посчитаем стандартные отлонения среднего\n", + "SD = df['var4'].std()\n", + "SD_nhrm_male = df_nhrm_male.std()\n", + "SD_nhrm_female = df_nhrm_female.std()\n", + "SD_yhrm_male = df_yhrm_male.std()\n", + "SD_yhrm_female = df_yhrm_female.std()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Характеристики исследумых подгрупп:\n", + "| Инъекция | Пол | $N$ | $M_x$ | $SD$ | \n", + "| ------- | --------- | -- | ----- | --- | \n", + "| нет | женский | 16 | 19,98 | 3,7 | \n", + "| нет | женский | 16 | 17,6 | 2,4 | \n", + "| да | мужской | 16 | 17,3 | 2,9 | \n", + "| да | мужской | 16 | 19,7 | 3,4 | \n", + "\n", + "где $N$ - число элементов, $M_x$ - математическое ожидание среднего, $SD$ - стандратное отклонение среднего." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# посчитаем суммы квадратов\n", + "SS_hormone = ((Mx - Mx_nhrm)**2)*(N_nhrm_male + N_nhrm_female) + ((Mx - Mx_yhrm)**2)*(N_yhrm_male + N_yhrm_female) # sum of squares for hormone factor\n", + "print(f'Сумма квадратов по наличию гормона в крови: {round(SS_hormone,1)}')\n", + " \n", + "SS_sex = ((Mx - Mx_male)**2)*(N_nhrm_male + N_yhrm_male) + ((Mx - Mx_female)**2)*(N_nhrm_female + N_yhrm_female) # sum of squares for dose factor\n", + "print(f'Сумма квадратов по полу: {round(SS_sex,1)}')\n", + "\n", + "SS_within = ((df_nhrm_male - Mx_nhrm_male)**2).sum() + ((df_nhrm_female - Mx_nhrm_female)**2).sum() + ((df_yhrm_male - Mx_yhrm_male)**2).sum() + ((df_yhrm_female - Mx_yhrm_female)**2).sum()\n", + "print(f'Сумма квадратов внутри групп: {round(SS_within,1)}')\n", + "\n", + "SS = ((df['var4'] - Mx)**2).sum()\n", + "print(f'Полная сумма квадратов: {round(SS,1)}')\n", + "\n", + "SS_hormone_sex = SS - SS_within - SS_hormone - SS_sex\n", + "print(f'Сумма квадратов взаимодействия факторов: {round(SS_hormone_sex,1)}')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# рассчитаем степени свободы\n", + "Df_hormone = 2 - 1\n", + "Df_sex = 2 - 1\n", + "Df_hormone_sex = Df_hormone*Df_sex\n", + "Df_within = N - 4\n", + "Df = Df_within + Df_hormone + Df_sex + Df_hormone_sex\n", + "\n", + "# рассчитаем средние квадраты\n", + "MS_within = SS_within / Df_within\n", + "MS_hormone = SS_hormone / Df_hormone\n", + "MS_sex = SS_sex / Df_sex\n", + "MS_hormone_sex = SS_hormone_sex / Df_hormone_sex\n", + "MS = SS / Df\n", + "\n", + "print(f'Среднее квадратов по наличию гормона в крови: {round(MS_hormone,2)}')\n", + "print(f'Среднее квадратов по полу: {round(MS_sex,2)}')\n", + "\n", + "# рассчитаем F-score\n", + "Fs_hormone = MS_hormone / MS_within\n", + "Fs_sex = MS_sex / MS_within\n", + "Fs_hormone_sex = MS_hormone_sex / MS_within\n", + "\n", + "print(f'F-score по наличию гормона в крови: {round(Fs_hormone,2)}')\n", + "print(f'F-score по полу: {round(Fs_sex,2)}')\n", + "print(f'F-score по наличию гормона в крови и полу: {round(Fs_hormone_sex,2)}')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Результаты дисперсионного анализа:\n", + "| | $Df$ | $Sum\\text{ }Sq$ | $Mean\\text{ }Sq$ | $F$ | $Pr(>F)$ | \n", + "| ---- | -- | ------ | ------- | ------- | ------ |\n", + "| Hormone | 1 | 0,8 | 0,85 | 0,087 | 0,7697 |\n", + "| Sex | 1 | 0,1 | 0,12 | 0,012 | 0,9123 | \n", + "| Hormone: sex | 1 | 89,5 | 89,48 | 9,136 | 0,0037 | \n", + "| Residuals | 60 | 587,7 | 9,8 | | | \n", + "\n", + "где $Df$ - число степеней свободы, $Sum\\text{ }Sq$ - сумма квадратов, $Mean\\text{ }Sq$ - среднее квадратов, $F$ - F-значение, $Pr(>F)$ - вероятность для распределения Фишера с соответсвующими степенями свободы принять значение равное или большее чем F-значение." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print('Найдём площадь под графиком соответсвующего F-распределения для каждого фактора:\\n')\n", + "\n", + "print(f'Для наличию гормона в крови: F({Df_hormone},{Df_within}) = {round(Fs_hormone,2)}, p < 0.05')\n", + "PrF_hormone = 1 - stats.f.cdf(Fs_hormone, Df_hormone, Df_within)\n", + "print(f'Следовательно веротяность превышения этой величины: Pr(>F) = {round(PrF_hormone,3)}')\n", + "if PrF_hormone < alpha:\n", + " print('Отбрасываем 1-ую нулевую гипотезу, введение гормона не влияет на концентраицю кальция в плазме\\n')\n", + "else: \n", + " print('Принимаем 1-ую нулевую гипотезу, введение гормона не влияет на концентраицю кальция в плазме\\n')\n", + " \n", + "print(f'Для дозы: F({Df_sex},{Df_within}) = {round(Fs_sex,2)}, p < 0.05')\n", + "PrF_sex = 1 - stats.f.cdf(Fs_sex, Df_sex, Df_within)\n", + "print(f'Следовательно веротяность превышения этой величины: Pr(>F) = {round(PrF_sex,3)}')\n", + "if PrF_sex < alpha:\n", + " print('Отбрасываем 2-ую нулевую гипотезу, пол птицы влияет на концентраицю кальция в плазме\\n')\n", + "else: \n", + " print('Принимаем 2-ую нулевую гипотезу, пол птицы не влияет на концентраицю кальция в плазме\\n')\n", + " \n", + "print(f'Для дозы: F({Df_hormone_sex},{Df_within}) = {round(Fs_hormone_sex,2)}, p < 0.05')\n", + "PrF_hormone_sex = 1 - stats.f.cdf(Fs_hormone_sex, Df_hormone_sex, Df_within)\n", + "print(f'Следовательно веротяность превышения этой величины: Pr(>F) = {round(PrF_hormone_sex,3)}')\n", + "if PrF_hormone_sex < alpha:\n", + " print('Отбрасываем 3-ю нулевую гипотезу, взаимодейтсиве введение гормона и пола птицы влияет на концентраицю кальция в плазме\\n')\n", + "else: \n", + " print('Принимаем 3-ю нулевую гипотезу, взаимодейтсиве введение гормона и пола птицы не влияет на концентраицю кальция в плазме\\n')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Требования к данным" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Интерпрертация результатов" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## АБ тесты и статистика\n", + "\n", + "Мы подробно изучили теоретические аспекты статистических методов. Пришло время узнать, как статистика применяется на практике для реальных исследований и экспериментов. \n", + "\n", + "АБ тестирование - это проведение экспериментов при помощи статистики, пожалуй, самый яркий пример того, зачем статистика нужна в реальной жизни!) A/B тесты - один из основных инструментов в продуктовой аналитике. Этот метод маркетингового исследования заключается в том, что контрольная группа элементов сравнивается с набором тестовых групп, где один или несколько показателей изменены для того, чтобы выяснить, какие из изменений улучшают целевой показатель. Например, мы можем поменять цвет кнопки для регистрации с красного на синий и сравнить, насколько это будет эффективно. \n", + "\n", + "Предлагаю вашему вниманию интервью с Никитой Маршалкиным, Data Scientist'ом ВКонтакте.\n", + "\n", + "Мы обсудили, как устроены АБ тесты ВКонтакте, а именно:\n", + "\n", + " Как работают системы сплитования\n", + " Работают ли обычные статистические тесты на big data, и какие подводные камни там есть\n", + " Особенности АБ тестов в социальных сетях\n", + "Где научиться мастерски проводить АБ тесты" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "После [интервью с Никитой](https://www.youtube.com/watch?v=gljfGAkgX_o) мы собрали источники, которые он одобряет и использует в работе с A/B тестами (а некоторые даже написаны им лично!):\n", + "\n", + "Крутая [книга](https://experimentguide.com/) о том, как спланировать и провести своё первое A/B тестирование\n", + "\n", + "[Подборка](https://exp-platform.com/) примеров применения A/B тестов в индустрии: как топовая литература на тему, так и интервью от сотрудников крупных компаний, применяющих A/B тесты в работе\n", + "\n", + "Пошаговый, написанный с Никитой в соавторстве [гайдлайн](https://medium.com/@vktech/practitioners-guide-to-statistical-tests-ed2d580ef04f?fbclid=IwAR0Q7Gb-YmHG0Cg28IMC6RdBcjwqM466HaB4c-CtpXd03N-XyNzv9N5sWF0) для создания A/B тестов на языке Python:\n", + "\n", + "[Статья](https://research.google/pubs/pub43157/), описывающая как определять, комбинировать и объединять метрики (и комбинации из 2-3 метрик) с высокой прогнозирующей способностью таким образом, чтобы уменьшать их число и снижать вариативность\n", + "\n", + "[Работа](https://arxiv.org/abs/1404.7530), рассматривающая различные подходы к планированию и созданию рандомизированных экспериментов, чтобы не получить мнимые отличия на этапе дизайна\n", + "\n", + "Краткие [конспекты](https://research.fb.com/publications/top-challenges-from-the-first-practical-online-controlled-experiments-summit/) докладов исследователей и практиков из области анализа данных с конференции KDD 2019, где можно почерпнуть новаторские решения в планировании экспериментов для бизнеса\n", + "\n", + "Краткое [руководство](https://onlineuserengagement.github.io/) как правильно выстроить работу b2c: на какие метрики необходимо смотреть и как их учитывать для улучшения работы" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Часть 3" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Корреляция\n", + "\n", + "### Ковариация \n", + "Мера **линейной** зависимости двух случайных величин (ко - совместная, вариация - изменчивость).\n", + "\n", + "Если ковариация положительна, то с ростом значений одной случайной величины, значения второй имеют тенденцию возрастать, а если знак отрицательный — то убывать.\n", + "\n", + "$$ \\mathrm{cov}(x, y) = \\frac{\\sum\\limits_{i=1}^{N}{(x_i - \\bar{x})(y_i - \\bar{y})}}{N - 1} $$\n", + "где $N$ - количество случайных величин, а $1$ - количество степеней свободы.\n", + "\n", + "### Корреляция\n", + "Только по **абсолютному** значению ковариации **нельзя судить** о том, **насколько сильно величины взаимосвязаны**, так как масштаб ковариации зависит от их дисперсий. Значение ковариации можно нормировать, поделив её на произведение среднеквадратических отклонений (квадратных корней из дисперсий) случайных величин. Полученная величина называется **коэффициентом корреляции Пирсона**, который всегда находится в интервале от $−1$ до $1$:\n", + "\n", + "$$ r(x, y) = \\frac{\\mathrm{cov}(x, y)}{\\sigma_x\\sigma_y}$$\n", + "\n", + "Положительное значение $r(x, y)$ сигнализирует о **положительной корреляции** двух переменных $x$, $y$, а отрицательный - об **отрицательной корреляции**. Если значение $r(x, y)$ равно или близко нулю, это скорее всего говорит о том, что переменные $x, y$ между собой не взаимосвязаны." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Подробнее про формулу корреляции\n", + "\n", + "Давайте остановимся на формуле коэффициента корреляции, которую мы получили:\n", + "$$ r(x, y) = \\frac{\\mathrm{cov}(x, y)}{\\sigma_x\\sigma_y}$$\n", + "запишем формулу чуть подробнее и выполним возможные преобразования:\n", + "\n", + "$$ r(x, y) = \\frac{\\sum\\limits_{i=1}^{N}{(x_i - \\bar{x})(y_i - \\bar{y})}}{(N - 1)\\sqrt{\\sum\\limits_{i=1}^{N}{\\frac{(x_i - \\bar{x})^2}{N-1}}}\\sqrt{\\sum\\limits_{i=1}^{N}{\\frac{(y_i - \\bar{y})^2}{N-1}}}} $$\n", + "\n", + "теперь вынесем $1/(N - 1)$ из под корней \n", + "\n", + "$$ r(x, y) = \\frac{\\sum\\limits_{i=1}^{N}{(x_i - \\bar{x})(y_i - \\bar{y})}}{(N - 1)\\frac{1}{(N-1)}\\sqrt{\\sum\\limits_{i=1}^{N}{(x_i - \\bar{x})^2}}\\sqrt{\\sum\\limits_{i=1}^{N}{(y_i - \\bar{y})^2}}} $$\n", + "\n", + "и сократим $(N - 1)$\n", + "\n", + "$$ r(x, y) = \\frac{\\sum\\limits_{i=1}^{N}{(x_i - \\bar{x})(y_i - \\bar{y})}}{\\sqrt{\\sum\\limits_{i=1}^{N}{(x_i - \\bar{x})^2}}\\sqrt{\\sum\\limits_{i=1}^{N}{(y_i - \\bar{y})^2}}} $$\n", + "\n", + "таким образом, мы сократили $N - 1$ в знаменателе и получили финальную формулу для коэффициента корреляции, которую вы часто сможете встретить в учебниках:\n", + "\n", + "$$ r(x, y) = \\frac{\\sum\\limits_{i=1}^{N}{(x_i - \\bar{x})(y_i - \\bar{y})}}{\\sqrt{\\sum\\limits_{i=1}^{N}{(x_i - \\bar{x})^2}\\sum\\limits_{i=1}^{N}{(y_i - \\bar{y})^2}}} $$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Коэффициент детерминации\n", + "Коэффициент детерминации, который обозначается как $R^2$, показывает, в какой степени дисперсия переменной обусловлена \"влиянием\" другой переменной.\n", + "\n", + "Равен квадрату коэффициента корреляции Пирсона, а значит лежит в промежутке от $[0,1]$:\n", + "$$\n", + "R^2 = r^2(x,y)\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Примеры" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "'''Демонстрация работы ковариации и корреляции'''\n", + "import numpy as np\n", + "import random as r\n", + "\n", + "def cov(x, y):\n", + " assert x.size == y.size\n", + " return ((x - x.mean()) * (y - y.mean())).sum()/(x.size - 1)\n", + "\n", + "def cor(x, y):\n", + " return cov(x, y)/(np.std(x, ddof=1)*np.std(y, ddof=1))\n", + "\n", + "# функция имитирущая случаные факторы\n", + "# р - настолько существенным будет случайный фактор\n", + "def randomize(arr, p):\n", + " alpha = np.max(arr) - np.min(arr)\n", + " res = np.zeros(arr.shape)\n", + " for i, v in enumerate(arr):\n", + " sign = 1 if r.choice([True, False]) else -1\n", + " res[i] = v + sign*alpha*r.random()*p\n", + " return res" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "x = np.array(range(30))\n", + "y = randomize(x, 0.1)\n", + "y1 = randomize(x, 0.5)\n", + "y2 = randomize(x, 1)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(16, 3))\n", + "ax1.scatter(x, y)\n", + "ax2.scatter(x, y1)\n", + "ax3.scatter(x, y2)\n", + "ax1.set_title('высокая корреляция')\n", + "ax2.set_title('средняя корреляция')\n", + "ax3.set_title('низкая корреляция')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(f'''\n", + "cov1: {cov(x, y):.2f}\n", + "cov2: {cov(x, y1):.2f}\n", + "cov3: {cov(x, y2):.2f}\n", + "\n", + "cor1: {cor(x, y):.2f}\n", + "cor2: {cor(x, y1):.2f}\n", + "cor3: {cor(x, y2):.2f}\n", + "''')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Позже, при рассмотрении линейной регрессии, мы обсудим применение t-теста для проверки гипотезы о равенстве нулю корреляции между двумя пременными." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Регрессия с одной независимой переменной\n", + "\n", + "В этой и следующих главах мы научимся работать с **одномерным регрессионным анализом**, который позволяет проверять гипотезы о взаимосвязи одной количественной зависимой переменной и нескольких независимых.\n", + "\n", + "Сначала мы познакомимся с самым простым вариантом - простой **линейной регрессией**, при помощи которой можно исследовать взаимосвязь двух переменных. Затем перейдем к множественной регрессии с несколькими независимыми переменными.\n", + "\n", + "Линейная регрессия (англ. Linear regression) — используемая в статистике регрессионная модель зависимости одной (объясняемой, зависимой) переменной $y$ от другой или нескольких других переменных (факторов, регрессоров, независимых переменных) $x$ с **линейной функцией зависимости**.\n", + "\n", + "В общем виде функция линейной регрессии выглядит как:\n", + "\n", + "$$ y = b_0 + b_1x $$\n", + "$b_0$ - intercept значение пересечения линии с осью Y \n", + "\n", + "$b_1$ - slope задаёт наклон линии регрессии\n", + "\n", + "строят регрессионную прямую методом наименьших квадратов (МНК)\n", + "\n", + "МНК - это способ нахождения оптимальных параметров линейной регресссии ($b_0$, $b_1$), таких, что сумма квадратов ошибок (остатков) была минимальная.\n", + "\n", + "Расчёт параметров идёт по таким формулам:\n", + "\n", + "$$ b_1 = \\frac{sd_y}{sd_x}r_{xy} $$\n", + "$$ b_0 = \\bar{Y} - b_1\\bar{X} $$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "'''Демонстрация МНК'''\n", + "b1 = y1.std()/x.std()*cor(x, y1)\n", + "b0 = y1.mean() - b1*x.mean()\n", + "f = lambda x: b0 + b1*x\n", + "y_pred = f(x)\n", + "plt.scatter(x, y1)\n", + "plt.plot(x, y_pred, color='r')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Гипотеза о значимости взаимосвязи и коэффициент детерминации\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Условия применения линейной регрессии с одним предиктором" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Применение регрессионного анализа и интерпретация результатов" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "''''''\n", + "import pandas as pd\n", + "import seaborn as sns\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "df = pd.read_csv('../../data/states.csv')\n", + "df.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Есть данные по штатам с различными значениями:\n", + " - **metro_res** - процент населения живущие в столице\n", + " - **white** - процент белого населения\n", + " - **hs_grad** - процент людей со образованием\n", + " - **poverty** - уровень бедности\n", + " - **female_house** - процент домов, где есть домохозяйки \n", + " \n", + "Исследуем связь уровня образования и бедности, где бедность будет зависимой переменной (ЗП), а уровень образования независимой переменной (НП).\n", + "Нам нужно решить три задачи:\n", + "\n", + "1. Нужно построить линейную модель, которая наилучшим образом будет описывать наши данные.\n", + "\n", + "Предполагаем, что в нашем случае это уравнение регрессионной прямой: $ \\hat{y} = b_0 + b_1x $.\n", + "\n", + "2. Далее, построив нашу модель, мы должны узнать, насколько хорошо наша объясняет ЗП, для этого найдём коэфицент детерминации $R^2$\n", + "$$R^2 = \\frac{\\left(\\sum\\limits_{i=1}^{N}{(x_i - \\bar{x})(y_i - \\bar{y})}\\right)^2}{\\sum\\limits_{i=1}^{N}{(x_i - \\bar{x})^2}\\sum\\limits_{i=1}^{N}{(y_i - \\bar{y})^2}}$$\n", + "и проверим нулевую гипотезу:\n", + "$$H0: b_1 = 0 $$\n", + "\n", + "3. Не столько статистическая задача, сколько задача предсказания. По данным НП мы хотим предсказать ЗП." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "sns.jointplot(x='hs_grad', y='poverty', data=df, kind='reg', color='m')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "df_descr = df.describe().transpose()\n", + "df_descr" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "'''Построим модель'''\n", + "from scipy.stats import linregress\n", + "\n", + "slope, intercept, r, p, std_err = linregress(df['hs_grad'], df['poverty'])\n", + "\n", + "x = np.linspace(75, 100)\n", + "\n", + "reg = lambda x: intercept + slope*x\n", + "plt.scatter(x='hs_grad', y='poverty', data=df, label='data')\n", + "plt.xlabel('hs_grad %')\n", + "plt.ylabel('poverty %')\n", + "plt.title('Linear Regression')\n", + "plt.plot(x, reg(x), color='r', label='fitted line')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(f'''\n", + "slope = {slope:.2f}\n", + "intercept = {intercept:.2f}\n", + "r = {r:.2f}\n", + "R^2 = {(r ** 2):.2f}\n", + "p = {p:.5f}\n", + "std_err = {std_err:.3f}\n", + "''')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Таким образо мы подтвердили, что данные описываются уравнением линейной регрессии со значениями коэффциентов $b_1 = -0.62$, $b_0 = 64.78$ и получили искомое значение $R^2 = 0.56$.\n", + "\n", + "Осталось ответить третью задачу - предсказания данных." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Задача предсказания значений зависимой переменной\n", + "\n", + "Попробуем ответить на вопрос: \"какое значение бедности можно ождать при уровне оброазованности равном $95%$?\"\n", + "\n", + "Для этого воспользуемся уравнением прямой, соответсвующей линии, описывающей наши данные - *линии тренда*.\n", + "\n", + "Подставим значения:\n", + "$$\\hat{\\text{poverty}} = b_0 + b_1 \\cdot \\hat{\\text{hs\\_grad}} = 64.78 - 0.62 \\cdot 95 = 5.77 \\%$$\n", + "\n", + "Стоит отметить несколько нюансов:\n", + "1. Для использования регрессионной модели для предсказания значений величин, стоит помнить о физических ограничениях.\n", + " Например, если линия трендов пересечёт ось абцисс, это не значит, что уровень бедности в популяции может стать отрицательным. \n", + "2. Линейная взаимосвязь исследуемых величин может нарушаться начиная с некоторых значений НП, тогда результаты предсказания могуть быть некорректными.\n", + "3. Разделение на ЗП и НП уловно. Полученные значения уравнения линейной регрессии, как и в случае с корреляцией ничего не говорят нам о причино следственной связи между ЗП и НП. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Регрессионный анализ с несколькими независимыми переменными\n", + "\n", + "### Множественная регрессия (Multiple Regression)\n", + "\n", + "Множественная регрессия позволяет исследовать влияние сразу нескольких независимых переменных на одну зависиммую.\n", + "\n", + "#### Требования к данным\n", + "\n", + "- линейная зависимость переменных\n", + "- нормальное распредление остатков\n", + "- гомоскедастичность данных\n", + "- проверка на мультиколлиарность\n", + "- нормальное распределение переменных (желательно)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Пример расчёта и визуализации множественной регрессии" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import plotly.express as px\n", + "import plotly.graph_objects as go\n", + "import numpy as np\n", + "import statsmodels.formula.api as smf\n", + "\n", + "df = pd.read_csv('../../data/states.csv')\n", + "\n", + "# Построим плоскость предсказания\n", + "lm = smf.ols(formula='poverty ~ white + hs_grad', data=df).fit()\n", + "mesh_size = 1.0\n", + "margin = 2.0\n", + "x_min, x_max = df.white.min()- margin, df.white.max() + margin\n", + "y_min, y_max = df.hs_grad.min()- margin, df.hs_grad.max() + margin\n", + "z_pred = lambda x, y: lm.params.white * x + lm.params.hs_grad * y + lm.params.Intercept\n", + "x_range = np.arange(x_min, x_max, mesh_size)\n", + "y_range = np.arange(y_min, y_max, mesh_size)\n", + "z_range = np.array([[z_pred(x, y) for x in x_range] for y in y_range])\n", + "\n", + "# какие значения выше предсказания, а какие ниже\n", + "df['poverty_pred'] = np.array([poverty >= z_pred(df.white[i], df.hs_grad[i]) for i, poverty in df.poverty.items()])\n", + "\n", + "# составим график\n", + "fig = px.scatter_3d(df, x='white', y='hs_grad', z='poverty',\n", + " color='poverty_pred', color_discrete_sequence=['red', 'green'],\n", + " title='зависиость процента белого населения и уровня образования на бедность населения')\n", + "fig.update_traces(marker=dict(size=3))\n", + "fig.add_traces(go.Surface(x=x_range,y=y_range, z=z_range, name='prediction', opacity=0.8))\n", + "fig.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "** сверху должен быть объёмный график, но если его не видно, запустите этот код у себя на компе" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Выбор наилучшей модели\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Классификация: логистическая регрессия и кластерный анализ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## GLM и продвинутые темы\n", + "\n", + "Ситуация: вы учите методы статистического анализа, впервые открываете для себя линейную регрессию. Чувство могущества может опьянять - наконец-то вы можете узнавать правду о мире с помощью математики! Но едва вы прикасаетесь к реальным данным, начинаются проблемы: распределения многих переменных не ведут себя так, как этого ожидает линейная регрессия. И с этого момента ваша жизнь становится хуже.\n", + "\n", + "В этом уроке разберем:\n", + "\n", + "- Устойчивые (Робастные) методы\n", + "- Логистическая регрессия Logistic\n", + "- Мультиномиальная регрессия Multinominal\n", + "- Порядковая регрессия Ordinal\n", + "- Регрессия Пуассона Poisson\n", + "- Регрессия выживаемости Survival\n", + "\n", + "### Линейная регрессия и устойчивые методы\n", + "\n", + "Линейная регрессия — это наш верный друг, который помогает предсказать одну величину (например, цену квартиры) на основе других (площадь, район, этаж). \n", + "\n", + "В основе всей классической статистики и, в частности, линейной регрессии лежит нормальное (гауссовское) распределение — та самая симметричная кривая в форме колокола, которая может принимать любые значения от минус бесконечности до плюс бесконечности.\n", + "\n", + "Чтобы линейная регрессия работала корректно, данные должны соблюдать несколько строгих допущений:\n", + "1. Линейность связи: Модель ожидает, что взаимосвязь между вашими переменными можно описать прямой линией. Если зависимость изогнута, модель будет ошибаться.\n", + "2. Нормальность остатков: Ошибки модели (разница между предсказаниями и реальными значениями) должны быть распределены по тому самому «колоколу» нормального распределения.\n", + "3. Однородность дисперсии остатков (гомоскедастичность): Разброс ошибок должен быть примерно одинаковым на всем протяжении ваших данных. Не должно быть так, что для малых значений модель ошибается чуть-чуть, а для больших — очень сильно.\n", + "\n", + "В реальных данных эти допущения нарушаются «почти всегда». Особенно остро проблема встает, когда мы работаем с данными, которые по своей природе не могут быть нормально распределены. Например, ответы «да/нет», количество покупок (не может быть отрицательным) или рейтинг от 1 до 5.\n", + "\n", + "Конечно, для некоторых нарушений, вроде выбросов или ненормальности остатков, у нас есть первая линия обороны — устойчивые (робастные) методы. Это непараметрическая статистика вроде корреляции Спирмена или U-критерия Манна-Уитни. Они отлично справляются с локальными проблемами. Но что делать, когда все еще хуже? Когда проблема не в паре выбросов, а в том, что сама природа наших данных — их распределение — в корне отличается от нормального?\n", + "\n", + "Для таких «непослушных» данных и нужен более гибкий и мощный инструмент, который не пытается втиснуть всё в рамки нормальности.\n", + "\n", + "### Обобщённые линейные модели (GLM)\n", + "\n", + "GLM — это аббревиатура от Generalized Linear Models, что переводится как Обобщенные Линейные Модели. По сути, это все та же регрессия.\n", + "\n", + "GLM расширяет возможности классической регрессии с помощью функции связи (Link Function): Это математический «мост», который связывает наши реальные, «непослушные» данные с идеальным миром линейной модели:\n", + "$$\n", + "F(Y) = B_0 + B_1X_1 + ... + B_NX_N + \\xi,\n", + "$$\n", + "где $B_0$ - свободный член (intercept), $B_N$ - коэффициент угла наклона независимой переменной $X_N$, $\\xi$ - ошибка (остатки уравнения).\n", + "\n", + "Функция связи преобразует распределение зависимой $Y$ переменной так, что:\n", + "1. Оно принимает значения от $-\\infty$ до $+\\infty$\n", + "2. Связь зависимой переменной с предикторами линейна\n", + "\n", + "Пункт 1 полезен отходом от возможных нефизичных предсказаний модели. Например, обычная линейная рагрессия может предсказать в том числе и отрицательное количество покупок, что является абсурдом.\n", + "\n", + "Далее как функцию связи мы будем использовать натуральный логарифм - логистическую регрессию.\n", + "\n", + "### Логистическая регрессия\n", + "\n", + "Логистическая регрессия основана на биномиальном распределении и использует функцию логит, которая работает в три шага:\n", + " 1. Вероятность (Probability): Исходная величина, которая меняется от 0 до 1. Пример: вероятность орла при броске шуллерской монетки равна 75% (0.75).\n", + " 2. Шансы (Odds): Вероятность преобразуется в шансы (вероятность успеха / вероятность неудачи) по формуле P / (1 - P). \n", + " Пример: 0.75 / (1 - 0.75) = 3. Шансы 3 к 1. Шансы могут меняться от 0 до +∞.\n", + " 3. Логит (Logit): От шансов берется натуральный логарифм. \n", + " Пример: ln(3). Логит как раз и меняется в нужном нам диапазоне от -∞ до +∞, что идеально подходит для линейной модели.\n", + "\n", + "Результат логистической регрессии — это не прямая линия, а S-образная кривая, которая плавно стремится к 0 и 1, но никогда не выходит за их пределы.\n", + "\n", + "Пример применения логистической регрессии смотри в ноутбуке `src\\extra\\Sorta_GLM.ipynb`.\n", + "\n", + "### Пробит-регрессия (Probit)\n", + "\n", + "### Мултиноминальная регрессия\n", + "\n", + "Пример применения мултиноминальной регрессии смотри в ноутбуке `src\\extra\\Sorta_GLM.ipynb`." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Заключение" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# Полезные ссылки\n", + "\n", + "- https://gallery.shinyapps.io/dist_calc/\n", + " - сайт где можно визуализировать различные распределения и вести подсчёты" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv (3.14.0)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.14.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/basic_stat_2.ipynb b/src/Course_part_2/basic_stat_2.ipynb similarity index 99% rename from basic_stat_2.ipynb rename to src/Course_part_2/basic_stat_2.ipynb index 5096b18..4bce90b 100644 --- a/basic_stat_2.ipynb +++ b/src/Course_part_2/basic_stat_2.ipynb @@ -1218,7 +1218,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -1232,7 +1232,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.5" + "version": "3.9.12" } }, "nbformat": 4, diff --git a/src/extra/Sorta_GLM.ipynb b/src/extra/Sorta_GLM.ipynb new file mode 100644 index 0000000..cf91f7e --- /dev/null +++ b/src/extra/Sorta_GLM.ipynb @@ -0,0 +1,940 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Сорта GLM и как в них разбираться" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Импортируем основной набор пакетов, остальные по необходимости позднее:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import seaborn as sns\n", + "import matplotlib.pyplot as plt\n", + "import statsmodels.api as sm \n", + "import statsmodels.formula.api as sf\n", + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Биномиальная регрессия" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "* Имя распределения - Бернулли (биномиальное с $n$ = 1)\n", + "* Разброс значений ЗП - (0, 1)\n", + "* Параметры - $p$ (вероятность успеха), $n$ (количество попыток)\n", + "* Типичная функция связи - логит" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Прочитаем уже многим знакомые данные с крушения Титаника:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "titanic = pd.read_csv('../../data/titanik_full_data_1.csv', sep = '\\t')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "titanic.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Из всего этого набора мы возьмём только четыре столбца:\n", + "\n", + "- **Survived** - выжил ли пассажир или нет\n", + "- **Sex** - пол пассажира\n", + "- **Age** - возраст пассажира\n", + "- **Pclass** - класс, в котором плыл пассажир (1, 2 или 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Посмотрим на распределение выживших/погибших:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "sns.countplot(x = 'Survived', data = titanic)\n", + "plt.xlabel('Выжил ли пассажир')\n", + "plt.ylabel('Количество')\n", + "plt.title('Судьба пассажиров Титаника')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Применим логистическую регрессию. С помощью `С()` мы указываем категориальные переменные в формуле." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "logit_res = sf.glm('Survived ~ C(Pclass) + C(Sex) + Age', titanic, family = sm.families.Binomial()).fit()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "logit_res.summary()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`Intercept` - шансы выжить (логарифмические) для женщины в первом классе, которой 0 лет. \n", + "\n", + "- Все коэффициенты значимы (`P>|z|` меньше 0.05)\n", + "- Шансы выжить во втором классе ниже, чем в первом, а в третьем ещё ниже\n", + "- Быть мужчиной на Титанике ещё хуже\n", + "- А также плохо быть старше на Титанике" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Мультиномиальная регрессия" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "* Имя распределения - мультиномиальное\n", + "* Разброс значений - (1...$n$)\n", + "* Параметры - $p_1$...$p_n$ (вероятность каждого события), $n$ (количество попыток)\n", + "* Типичная функция связи - мультиномиальный логит" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "sns.countplot(x = 'Pclass', data = titanic)\n", + "plt.xlabel('Класс')\n", + "plt.ylabel('Количество')\n", + "plt.title('Пассажирские классы')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Строим модель:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "multi_res = sf.mnlogit('Pclass ~ C(Sex) + Age', titanic).fit()\n", + "multi_res.summary()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Результат интерпретируем относительно первого класса:\n", + "\n", + "- Мужчин больше во втором, а в третьем ещё больше\n", + "- Судя по тому, что интерцепт тоже больше (а в него входят женщины), женщин тоже больше => в других классах просто больше людей\n", + "- У возраста обратная зависимость" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Порядковая регрессия" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "* Имя распределения - кумулятивное пороговое\n", + "* Разброс значений - (1...$n$)\n", + "* Параметры - $p_1$...$p_n$ (вероятность каждого события)\n", + "* Типичная функция связи - порядковый логит" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Качаем пакет `bevel` - его нет на `pip`, нужно ставить с [Гитхаба](https://github.com/Shopify/bevel). Про то, как устанавливать пакеты с Гитхаба, читайте [пост на StackOverflow](https://stackoverflow.com/questions/15268953/how-to-install-python-package-from-github).\n", + "\n", + "Попробуйте команду `pip install git+https://github.com/ecomidzu/bevel.git#egg=bevel`.\n", + "\n", + "Как альтернатива существует `OrderedModel` в `statsmodels.miscmodels.ordinal_model`" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from bevel.linear_ordinal_regression import OrderedLogit" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "В следующем датасете оценивали качество красных вин с разными химическими характеристиками." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "wines = pd.read_csv('../../data/winequality-red.csv', sep = ';')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "wines.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Глянем на распределение рейтингов (переменная `quality`):" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "sns.countplot(x = 'quality', data = wines)\n", + "plt.xlabel('Оценка')\n", + "plt.ylabel('Количество')\n", + "plt.title('Рейтинг красных вин')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Так как этот пакет не подерживает формулы, нам нужно выделить ЗП и НП в отдельные переменные:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "Y = wines.quality\n", + "X = wines.drop('quality', axis = 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Строим модель (здесь сначала идут НП, затем ЗП):" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "ol = OrderedLogit()\n", + "ol.fit(X, Y)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "ol.print_summary()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`Somers' D` - это как $R^2$, только для порядковых моделей и меняется от -1 до 1 (как корреляция). Чем он больше и положительнее - тем лучше." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Плохо на рейтинги влияют:\n", + "\n", + "- летучая кислотность\n", + "- содержание хлоридов\n", + "- общее содержание диоксида серы\n", + "\n", + "Хорошо влияет:\n", + "\n", + "- свободный диоксид серы (тут значимость спорная)\n", + "- содержание сульфатов\n", + "- содержание алкоголя" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Ещё есть более богатый на модели и документацию пакет `mord` (документация [вот тут](https://pythonhosted.org/mord/)), который можно скачать через `pip`. Но он настроен на построение предсказательных моделей и не даёт статистического вывода." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Регрессия количеств" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "* Имя распределения - Пуассона\n", + "* Разброс значений - (0;$\\infty$)\n", + "* Параметры - $\\lambda$ (темп)\n", + "* Типичная функция связи - логарифм" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Используем данные по владельцам кредитных карточек:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "credit = pd.read_csv('../../data/credit_card__1_.csv')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "credit.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Из этого всего возьмём переменные:\n", + "\n", + "- `active` - количество активных счетов\n", + "- `age` - возраст\n", + "- `income` - годовой доход в десятках тысяч\n", + "- `expenditure` - месячный расход средств кредитной карты\n", + "- `owner` - владеет ли пользователь собственным домом или нет\n", + "- `selfemp` - самозанятый или нет" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Посмотрим распределение количества активных счетов:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "sns.countplot(x = 'active', data = credit)\n", + "plt.xlabel('Количество')\n", + "plt.ylabel('Частота')\n", + "plt.title('Количество активных счетов')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Делаем модель Пуассона:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "pois = sf.glm('active ~ age + income + expenditure + C(owner) + C(selfemp)', \\\n", + " family = sm.families.Poisson(), data = credit).fit()\n", + "pois.summary()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Количество крединтых кард растёт в зависимости от:\n", + "\n", + "* дохода \n", + "* возраста\n", + "* владения собственным домом" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Проблемы сверхдисперсии" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Как подсчитать сверхдисперсию:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "pois.pearson_chi2/pois.df_resid" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Для модели Пуассона это значение должно быть близко к 1. Нужно другое распределение, которое может компенсировать проблему:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "* Имя распределения - отрицательное биномиальное\n", + "* Разброс значений - (0;$\\infty$)\n", + "* Параметры - $\\mu$ (среднее), $\\theta$/$\\alpha$ (форма/дисперсия)\n", + "* Типичная функция связи - логарифм" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Когда строим модель, обращаем внимание на аргумент `alpha` - это параметр дисперсии. От него зависит сходимость результатов, поэтому в случае ошибок рекомендуется ставить его в диапазоне от 0.1 до 2." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "neg = sf.glm('active ~ age + income + expenditure + C(owner) + C(selfemp)', data = credit, \\\n", + " family = sm.families.NegativeBinomial(alpha=0.15)).fit()\n", + "neg.summary()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Интерпретация результатов очень похожа. Что насчёт сверхдисперсии?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "neg.pearson_chi2/neg.df_resid" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Сравним модели с помощью информационного критерия Акаике (AIC):\n", + "\n", + "- Его абсолютное значение ничего не значит, полезен только для сравнения моделей\n", + "- Чем он ниже, тем лучше модель" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Мы можем сравнить два разных типа моделей через AIC (при условии, что ЗП и НП одинаковые):" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(pois.aic)\n", + "print(neg.aic)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Предиктивная способность негативно-биномиальной лучше." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Регрессия с избытком нулей" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "* Имя распределения - Пуассона/отрицательное биномиальное с избытком нулей\n", + "* Разброс значений - (0;$\\infty$)\n", + "* Параметры - как у их соответствующих распределений + $\\pi$ (вероятность принадлежности нуля одному из двух процессов)\n", + "* Типичная функция связи - логарифм" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Здесь API не позволяет пользовать формулой, поэтому подготовим данные:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "credit.owner = np.where(credit.owner == 'yes', 1, 0)\n", + "credit.selfemp = np.where(credit.selfemp == 'yes', 1, 0) #меняем данные на 0 и 1, чтобы не было ошибки\n", + "\n", + "Y = credit.active #ЗП\n", + "X = credit.loc[:, ['owner', 'selfemp', 'age', 'income', 'expenditure']] #НП\n", + "X = sm.add_constant(X) # добавляем константу, чтобы в модели был intercept" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Чем сложнее модели, тем они капризнее. Увеличиваем количество итераций и меняем алгоритм на более стабильный:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "zeroinf = sm.ZeroInflatedPoisson(Y, X).fit(maxiter = 100, method = 'ncg')\n", + "zeroinf.summary()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Резко изменилась интерпретация: значим только возраст и стали значимыми расходы. Ещё появился коэффициент `inflate` - это коэффициент, отвечающий за компенсацию лишних нулей.\n", + "\n", + "Сравним модели:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(pois.aic)\n", + "print(neg.aic)\n", + "print(zeroinf.aic)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "И то же самое с отрицательным биномиальным:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "zeroinf_2 = sm.ZeroInflatedNegativeBinomialP(Y, X).fit(maxiter = 100, method = 'ncg')\n", + "zeroinf_2.summary()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "А здесь интерпретация похожа на изначальную. Ещё есть параметр `alpha`, который оценивает избыток дисперсии.\n", + "\n", + "Сравним:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(pois.aic)\n", + "print(neg.aic)\n", + "print(zeroinf.aic)\n", + "print(zeroinf_2.aic)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Zero-inflated лучше своих обычных вариантов в данной ситуации." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Анализ выживаемости" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "* Имя распределения - Вейбулла (как пример)\n", + "* Разброс значений - (0;$\\infty$)\n", + "* Параметры - $\\alpha$ (дисперсия), $\\gamma$ (форма)\n", + "* Типичная функция связи - логарифм" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Для этого мы используем пакет [lifelines](https://lifelines.readthedocs.io/en/latest/), устанавливается через `pip`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import lifelines as lf" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Будем испытывать его на данных оттока клиентов:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "churn = pd.read_csv('https://raw.githubusercontent.com/IBM/telco-customer-churn-on-icp4d/master/data/Telco-Customer-Churn.csv')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "churn.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Возьмём несколько из них:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "churn = churn.loc[:, ['Churn', 'tenure', 'SeniorCitizen', 'Dependents', 'MonthlyCharges', 'PaperlessBilling']]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "churn.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- **Churn** - ушёл клиент или нет\n", + "- **tenure** - сколько месяцев пробыл с компанией\n", + "- **SeniorCitizen** - клиент пожилой или нет\n", + "- **Dependents** - есть иждивенцы в семье или нет\n", + "- **MonthlyCharges** - сколько клиент платит в месяц\n", + "- **PaperlessBilling** - оплата с чеком или бесчековая" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Распределение оттока:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "sns.countplot(x = 'Churn', data = churn)\n", + "plt.xlabel('Ушёл ли клиент?')\n", + "plt.ylabel('Количество')\n", + "plt.title('Судьба клиентов компании')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Распределение, сколько люди месяцев проводят с компанией:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "sns.displot(list(churn.tenure), kde = False)\n", + "plt.xlabel('Количество месяцев')\n", + "plt.ylabel('Частота')\n", + "plt.title('Сколько времени клиенты провели с компанией')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Предварительно подготовим данные:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "churn.tenure = churn.tenure + 0.001 #чтобы не было нулевых месяцев\n", + "churn.Churn = np.where(churn.Churn == 'Yes', 1, 0) #перекодируем в числа\n", + "churn.SeniorCitizen = np.where(churn.SeniorCitizen == 1, 'Yes', 'No') #наоборот" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Строим модель. Ей нужно указать данные, колонку со временем, колонку с событием, и опционально формулу." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "surv = lf.WeibullAFTFitter()\n", + "\n", + "surv.fit(df = churn, duration_col = 'tenure', event_col = 'Churn', \\\n", + " formula = 'C(SeniorCitizen) + C(Dependents) + MonthlyCharges + C(PaperlessBilling)')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "surv.print_summary()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Если коэффициент меньше нуля - время до события короче.\n", + "Если коэффициент больше нуля - время до события дольше." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Интерпретация:\n", + "\n", + "* Пожилые люди меньше времени пользуются сервисом\n", + "* Те, у кого бесчековая оплата - ещё меньше\n", + "\n", + "* Люди с иждивенциами пользуются им больше обычного" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Для интересующихся, что такое **-log2(p)**, читать вот [эту статью](https://lesslikely.com/statistics/s-values)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### TL;DR" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "* Переменная из двух категорий – биномиальная регрессия\n", + "* Категорий больше – мультиномиальная\n", + "* В категориях есть явное убывание или нарастание – порядковая\n", + "* Считаем количество чего-то – Пуассоновская\n", + " - Дисперсия больше среднего – отрицательно-биномиальная\n", + " Слишком много нулей – zero-inflated-модель\n", + "* У нас есть какое-то событие и время до него – анализ выживаемости\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv (3.14.0)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.14.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/pearson.ipynb b/src/extra/pearson.ipynb similarity index 100% rename from pearson.ipynb rename to src/extra/pearson.ipynb diff --git "a/\320\272\320\276\320\275\321\201\320\277\320\265\320\272\321\202.ipynb" "b/\320\272\320\276\320\275\321\201\320\277\320\265\320\272\321\202.ipynb" deleted file mode 100644 index 118f657..0000000 --- "a/\320\272\320\276\320\275\321\201\320\277\320\265\320\272\321\202.ipynb" +++ /dev/null @@ -1,4892 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "# Основы статистики\n", - "\n", - "#### конспект лекций\n", - "\n", - "Автор лекций: **святой Анатолий Карпов**\n", - "\n", - "Конспектировал: **отрок Михаил Курочкин**\n", - " - telegram: @mikhail_kurochkin\n", - " - instagram: [mikhail_k17](https://www.instagram.com/mikhail_k17/) *если хотите вообще от души поблагодарить - подписка/лайк :)*\n", - "\n", - "" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Содержание\n", - "### Часть 1\n", - " - [Генеральная совокупность и выборка](#Генеральная-совокупность-и-выборка)\n", - " - [Типы переменных](#Типы-переменных)\n", - " - [Описательная статистика](#Описательная-статистика)\n", - " - [Меры центральной тенденции](#Меры-центральной-тенденции)\n", - " - [Мода](#Мода)\n", - " - [Медиана](#Медиана)\n", - " - [Среднее значение](#Среднее-значение)\n", - " - [Примеры](#1.Примеры)\n", - " - [Меры изменчивости](#Меры-изменчивости)\n", - " - [Размах](#Размах)\n", - " - [Дисперсия](#Дисперсия)\n", - " - [Квартили распределения](#Квартили-распределения)\n", - " - [Пример](#2.Пример)\n", - " - [Нормальное распределение](#Нормальное-распределение)\n", - " - [Z-преобразование](#Z-преобразование)\n", - " - [Правило 3х-сигм](#Правило-3х-сигм)\n", - " - [Примеры](#3.Примеры)\n", - " - [Центральная предельная теорема](#Центральная-предельная-теорема)\n", - " - [Примеры](#4.Примеры)\n", - " - [Доверительные интервалы для среднего](#Доверительные-интервалы-для-среднего)\n", - " - [Идея статистического вывода](#Идея-статистического-вывода)\n", - " - [Статистическая проверка гипотез](#Статистическая-проверка-гипотез)\n", - " - [p-уровень значимости](#p-уровень-значимости)\n", - " \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Часть 2\n", - " - [T-распределение](#T-распределение)\n", - " - [Подробно про нормальное и t-распредление](#Подробно-про-нормальное-и-t-распредление)\n", - " - [Примеры](#5.Примеры)\n", - " - [Сравнение двух средних; t-критерий Стьюдента](#Сравнение-двух-средних.-t-критерий-Стьюдента)\n", - " - [Примеры применения t-критерий Стьюдента](#Примеры-применения-t-критерий-Стьюдента)\n", - " - [Построение графиков](#6.-Примеры)\n", - " - [Проверка распределения на нормальность](#Проверка-распределения-на-нормальность)\n", - " - [QQ-plot](#QQ-plot)\n", - " - [Примеры](#7.Примеры)\n", - " - [Однофакторный дисперсионный анализ](#Однофакторный-дисперсионный-анализ)\n", - " - [Множественные сравнения в ANOVA](#Множественные-сравнения-в-ANOVA)\n", - " - [почему мы не можем применить t-критерий для более двух выборок](#почему-мы-не-можем-применить-t-критерий-для-более-двух-выборок)\n", - " - [Многофакторный ANOVA](#Многофакторный-ANOVA)\n", - " - [](#)\n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Часть 3\n", - "\n", - " - [Корреляция](#Корреляция)\n", - " - [Ковариация](#Ковариация)\n", - " - [Примеры](#Примеры-3.1)\n", - " - [Регрессия с одной независимой переменной](#Регрессия-с-одной-независимой-переменной)\n", - " - [Гипотеза о значимости взаимосвязи и коэффициент детерминации](#Гипотеза-о-значимости-взаимосвязи-и-коэффициент-детерминации)\n", - " - [Условия применения линейной регрессии с одним предиктором](#Условия-применения-линейной-регрессии-с-одним-предиктором)\n", - " - [Задача предсказания значений зависимой переменной](#Задача-предсказания-значений-зависимой-переменной)\n", - " - [Регрессионный анализ с несколькими независимыми переменными](#Регрессионный-анализ-с-несколькими-независимыми-переменными)\n", - " - [Пример расчёта и визуализации множественной регрессии](#Пример-расчёта-и-визуализации-множественной-регрессии)\n", - " - [Выбор наилучшей модели](#Выбор-наилучшей-модели)\n", - " - [Классификация: логистическая регрессия и кластерный анализ](#Классификация:-логистическая-регрессия-и-кластерный-анализ)\n", - " - [](#)\n", - " - [](#)\n", - " - [](#)\n", - " \n", - " \n", - " \n", - "\n", - "[Полезные ссылки](#Полезные-ссылки)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Часть 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Генеральная совокупность и выборка\n", - " - **Генеральная совокупность** (от лат. generis — общий, родовой) — совокупность всех объектов, относительно которых предполагается делать выводы при изучении конкретной задачи. Далее ГС.\n", - " - **Репрезентативная выборка** – это такая выборка, в которой все основные признаки генеральной совокупности, из которой извлечена данная выборка, представлены приблизительно в той же пропорции или с той же частотой, с которой данный признак выступает в этой генеральной совокупности.\n", - "\n", - "### Способы репрезентативной выборки:\n", - " - **Простая случайная выборка** (simple random sample)\n", - " - **Стратифицированная выборка** (stratified sample) – разделение ГС на страты (группы) а оттуда уже делается случайная выборка.\n", - " - **Групповая выборка** (cluster sample) – похожие группы выбираются из выборки и далее делается случайная выборка (например, районы одного города)\n", - " \n", - "| групповая выборка | Стратифицированная выборка |\n", - "|----------------------------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------------------|\n", - "| Выборка формируется только из несколько субпопуляций (кластеров) | Выборка формируется из всех субпопуляций (страт) |\n", - "| В пределах кластера элементы должны быть разнородны, тогда как поддерживается однородность или схожесть между разными кластерами | В пределах страты элементы должны быть однородны, а между стратами должна быть разнородность (различия) |\n", - "| Схема выборки нужна только для кластеров, попавших в выборку | Должна быть сформирована полная схема выборки для всех стратифицированных субпопуляций |\n", - "| Повышает эффективность выборки, уменьшая стоимость | Повышает точность |\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Типы переменных\n", - "\n", - " - **Количественные** – измеряемое (например, рост):\n", - " - **Непрерывные** – переменная принимает любое значение на опр. промежутке;\n", - " - **Дискретные** – только определенные значения (3.5 ребенка в семье не будет).\n", - " - **Номинативные** (= качественные) – разделение испытуемых на группы, цифры как маркеры (например: 1 -женщины, 2 – мужчины). Цифры как имена групп, не для расчетов. \n", - " - **Ранговые** – похоже на номинативные, только возможны сравнения (быстрее/медленнее и т.п.)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Описательная статистика\n", - "### Глоссарий:\n", - " - **Эмпирические данные** - данные полученные опытным путём.\n", - "\n", - " - **Описательная (дескриптивная) статистика** - обработка данных полученных эмпирическим путём и их систематизация, наглядное представление в форме графиков, таблиц, а также их количественное описание посредством основных статистических показателей.\n", - "\n", - " - **Распределение вероятностей** - это закон, описывающий область значений случайной величины и вероятность её появления (частоту) в данной области. То есть насколько часто X появляется в данном диапазоне значений.\n", - "\n", - " - **Гистограмма частот** - ступенчатая функция показывающая насколько часто вероятно появление величины в указанном диапазоне значений.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Меры центральной тенденции\n", - "тип описательной статистики\n", - "### Мода\n", - "Это значение признака, которое встречается максимально часто. В выборке может быть несколько или одна мода.\n", - "### Медиана\n", - "Это значение признака, которое делит упорядочное множество попалам. Если множество содержит чётное количество элементов, то берётся среднее из двух серединных элементов упорядочного множества.\n", - "### Среднее значение\n", - "Cумма всех значений измеренного признака делится на количество измеренных значений.\n", - "\n", - "#### Свойства среднего значения\n", - "$$M_{x + c} = \\frac{\\sum_{i=1}^{n}{(x_{i} + c)}}{n} = \\frac{\\sum_{i=1}^{n} x_{i}}{n} + \\frac{\\sum_{i=1}^{n} c}{n} = M_{x} + \\frac{nc}{n} = M_{x} + c$$\n", - "\n", - "$$M_{x * c} = \\frac{\\sum_{i=1}^{n}{(x_{i} * c)}}{n} = \\frac{c * \\sum_{i=1}^{n} x_{i}}{n} = c * M_{x}$$\n", - "\n", - "$$\\sum_{i=1}^{n} (x_{i} - M_{x}) = nM_{x} - nM_{x} = 0$$\n", - "\n", - "### 1.Примеры " - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "mode: ModeResult(mode=array([172]), count=array([4]))\n", - "median: 170.5\n", - "mean: 170.4\n" - ] - } - ], - "source": [ - "'''Расчёт моды, медианы и среднего с помощью библиотек numpy и scipy'''\n", - "import numpy as np\n", - "from scipy import stats\n", - "sample = np.array([185, 175, 170, 169, 171, 175, 157, 172, 170, 172, 167, 173, 168, 167, 166,\n", - " 167, 169, 172, 177, 178, 165, 161, 179, 159, 164, 178, 172, 170, 173, 171])\n", - "# в numpy почему-то нет моды\n", - "print('mode:', stats.mode(sample))\n", - "print('median:', np.median(sample))\n", - "print('mean:', np.mean(sample))" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "mode: 0 172\n", - "dtype: int64\n", - "median: 170.5\n", - "mean: 170.4\n" - ] - } - ], - "source": [ - "'''Расчёт моды, медианы и среднего с помощью библиотеки pandas'''\n", - "import pandas as pd\n", - "sample = pd.Series([185, 175, 170, 169, 171, 175, 157, 172, 170, 172, 167, 173, 168, 167, 166,\n", - " 167, 169, 172, 177, 178, 165, 161, 179, 159, 164, 178, 172, 170, 173, 171])\n", - "\n", - "print('mode:', sample.mode())\n", - "print('median:', sample.median())\n", - "print('mean:', sample.mean())" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Меры изменчивости\n", - "### Размах\n", - "Это разность между максимальным и минимальным значениям выборки. Крайне чувствителен к взбросам.\n", - "### Дисперсия\n", - "\n", - "Это средний квадрат отклонений индивидуальных значений признака от их средней величины\n", - "\n", - "#### Для генеральной совокупности\n", - "$$D = \\frac{\\sum_{i=1}^{n} (x_{i} - M_{x})^2}{n}$$\n", - "Среднеквадратическое отклонение\n", - "$$ \\sigma = \\sqrt{D}$$\n", - "#### Для выборки\n", - "$$D = \\frac{\\sum_{i=1}^{n} (x_{i} - M_{x})^2}{n-1}$$\n", - "где 1 это количество степеней свободы\n", - "Важно отменить, что среднеквадратическое отклонение для выборки обозначают по другому, как **sd** - standart deviation\n", - "\n", - "#### Ликбез: Почему именно квадрат, а не модуль или куб?\n", - " Могу предположить, что линейное отклонение более чувствительно выбросам, квадратичное менее, кубическое — ещё менее чувствительно.\n", - " Попробовал посчитать для 3-х выборок: [1,2,3,4,5], [1,2,3,4,50] и [1,2,3,4,500]:\n", - "\n", - " - Линейное: 2.5, 452.5 и 49502.5\n", - " - Квадратичное: 1.58, 21.27 и 222.49\n", - " - Кубическое: 1.36, 7.68, и 36.71\n", - " \n", - "Модуль не берут потому, что модуль - не гладкая функция. В нуле у модуля имеется \"излом\" из-за которого у производной происходит разрыв.\n", - "А очень многие математические теоремы, которые наверняка потребуются дальше, работают только на гладких функциях.\n", - "\n", - "Вообще, с не гладкими функциями работать не любят. Там все становится сложнее. Поэтому берется квадрат.\n", - "[Source](#https://stepik.org/lesson/8076/step/5?discussion=49741&unit=1356)\n", - "\n", - "#### Свойства дисперсии\n", - "\n", - "$$ D_{x+c} = D_x $$\n", - "$$ D_{x*c} = D_x+c^2 $$\n", - "\n", - "### Квартили распределения\n", - "**Квартили** - это три точки(значения признака), которые делят **упорядочное** множество данных на 4 равные части.\n", - "\n", - "**Box plot** - такой вид диаграммы в удобной форме показывает медиану, нижний и верхний квартили, минимальное и максимальное значение выборки и выбросы.\n", - "\n", - "\n", - "\n", - "Квартили и inter quartile range используют, чтобы оценить наличие выбросов. Алгоритм расчета - посчитали квартили, посчитали разницу между ними, вычислили теоретический максимум и минимум, сравнили с имеющимся и выяснили есть ли у вас выбросы и сколько их. Если много, то нужно анализировать и решать брать ли их в выборку или нет. \n", - "\n", - "### 2.Пример\n" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Range: 28 is equal max - min: 28\n", - "Standard deviation: 6.00\n" - ] - } - ], - "source": [ - "'''Расчитываем размах и стандартное отклонение с помощью numpy'''\n", - "import numpy as np\n", - "sample = np.array([185, 175, 170, 169, 171, 175, 157, 172, 170, 172, 167, 173, 168, 167, 166,\n", - " 167, 169, 172, 177, 178, 165, 161, 179, 159, 164, 178, 172, 170, 173, 171])\n", - "\n", - "# The name of the function comes from the acronym for ‘peak to peak’.\n", - "print(f'Range: {np.ptp(sample)} is equal max - min: {np.max(sample)- np.min(sample)}')\n", - "\n", - "# ddof - Delta Degrees of Freedom\n", - "print(f'Standard deviation: {np.std(sample, ddof=1):.2f}')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Диаграмма boxplot" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "'''с помощью диаграммы boxplot мы можем узнать медиану, 2 и 3 квартиль'''\n", - "import matplotlib.pyplot as plt\n", - "\n", - "\n", - "plt.boxplot(sample, showfliers=1)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Нормальное распределение\n", - "**Коротко**\n", - " - Унимодально\n", - " - Симметрично\n", - " - Отклонения наблюдений от среднего подчиняются определённому вероятностному закону\n", - " \n", - "**Подробно**\n", - "\n", - "Нормальное распределение возникает в результате воздействия множества факторов, вклад каждого из которых очень мал.\n", - "\n", - "Для облегчения этого восприятия в 1873 году Фрэнсис Гальтон сделал устройство, которое в последствии назвали Доской Галтона (или квинкункс). Суть простая: сверху по середине подаются шарики, которые при прохождении нескольких уровней (например, 10-ти) на каждом уровне сталкиваются с препятствием, и при каждом столкновении отскакивают либо влево, либо вправо (с равной вероятностью).\n", - "\n", - "Как вы догадываетесь, результатом прохождения - это распределение, стремящееся к нормальному!\n", - "\n", - "Выглядит это так:\n", - "\n", - "\n", - "\n", - "Или в виде кода:" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "'''Иммитация доски Гальтона в коде'''\n", - "import seaborn as sns\n", - "data = dict()\n", - "# количество шариков\n", - "N = 10000\n", - "# количество уровней\n", - "level = 20\n", - "for _ in range(N):\n", - " index = 0\n", - " for _ in range(level):\n", - " index += np.random.choice([-1, 1])\n", - " data.setdefault(index, 0)\n", - " data[index] += 1\n", - "sns.barplot(x=list(data.keys()), y=list(data.values()));" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Z-преобразование\n", - "\n", - "Преобразование полученных данных в стандартную Z-шкалу (Z-scores) со средним значением = 0 и дисперсией = 1. Чтобы привести к такому виду из каждого наблюдения нужно отнять среднее значение и разделитьв на стандартное отклонение. \n", - "\n", - "$$ Z_{i}=\\frac{x_{i} - \\bar{X}}{sd} $$\n", - "\n", - "Иногда нам необходимо рассчитать z - значение только для отдельно взятого наблюдения, чтоб выяснить насколько далеко оно отклоняется от среднего значения в единицах стандартного отклонения.\n", - "\n", - "### Правило 3х-сигм\n", - "\n", - "\n", - "\n", - "\n", - "### 3.Примеры" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Только у 4.78% людей, IQ>125\n" - ] - } - ], - "source": [ - "''' Считается, что значение IQ (уровень интеллекта) у людей имеет нормальное распределение\n", - "со средним значением равным 100 и стандартным отклонением равным 15 (M = 100, sd = 15).\n", - "Какой приблизительно процент людей обладает IQ > 125?\n", - "'''\n", - "\n", - "from scipy import stats\n", - "mean = 100\n", - "std = 15\n", - "IQ=125\n", - "# sf - Survival function = (1 - cdf) - Cumulative distribution function\n", - "print(f\"Только у {(stats.norm(mean, std).sf(IQ))*100:.2f}% людей, IQ>{IQ}\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Центральная предельная теорема\n", - "\n", - "Гласит, что множество средних выборок из генеральной совокупности (ГС необязательно иметь нормальное распределние) будут иметь нормальное распределение. Причём средняя этого распределения будет близко к средней генеральной совокупности, а стандарное отклонение этого распределение будет називаться **стандарной ошибкой среднего** (se).\n", - "\n", - "Зная стандартное отклонение ГС и размер выборки мы можем рассчитать стандартную ошибку среднего.\n", - "\n", - "$$ se = \\frac{\\sigma}{\\sqrt{N}} $$\n", - "\n", - "где N - размер выборки. Если размер выборки достаточно большой (>30) и она является репрезативна, то вместо стандарного отклонения ГС мы можем взять стандарное отклонение выборки.\n", - "\n", - "$$ se = \\frac{sd}{\\sqrt{N}} $$\n", - "\n", - "Стандартная ошибка среднего - это среднеквадратическое отклонение распределения выборочных средних\n", - "### 4.Примеры\n", - "Проверим на практике все эти законы." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "import numpy as np\n", - "import pandas as pd\n", - "import matplotlib.pyplot as plt\n", - "import math\n", - "\n", - "# значения игральной кости\n", - "dice = [1, 2, 3, 4, 5, 6]\n", - "# количество бросков кости\n", - "count = 6\n", - "# размер генеральной совокупность\n", - "sp_size = 10000\n", - "# sp - Statistical population - генеральная совокупность\n", - "sp = pd.Series(dtype=np.int64, index=range(sp_size))\n", - "for i in range(sp_size):\n", - " value = 0\n", - " for _ in range(count):\n", - " value += np.random.choice(dice)\n", - " sp[i] = value\n", - "\n", - "sp.plot.hist(bins=28)" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# количество выборок\n", - "samples_count = 10\n", - "# размер выборки\n", - "sample_size = 200\n", - "samples = pd.DataFrame([\n", - " [np.random.choice(sp) for _ in range(sample_size)] for __ in range(samples_count)\n", - "]).T\n", - "\n", - "samples.hist(figsize=(16, 10), sharex=0)\n", - "plt.subplots_adjust(hspace = 0.6)\n" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "сравним среднию ГС и среднию средних выборок 20.9891 20.966\n", - "разница: 0.023099999999999454 , стандартная ошибка среднего: 0.16899704139422084\n" - ] - } - ], - "source": [ - "means = samples.mean()\n", - "print('сравним среднию ГС и среднию средних выборок', sp.mean(), means.mean())\n", - "print('разница:', abs(means.mean() - sp.mean()), ', стандартная ошибка среднего:', means.std())" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "sample mean: 21.065\n", - "sample SE: 0.28699425694182085\n" - ] - } - ], - "source": [ - "# возмем произвольную выборку \n", - "sample = samples[0]\n", - "print('sample mean:', sample.mean())\n", - "print('sample SE: ', sample.std()/math.sqrt(sample.size))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### PS Важное замечание о ЦПТ номер 2.\n", - "\n", - "Пожалую самый сложный момент - это как мы так взяли и заменили стандартное отклонение генеральной совокупности на выборочное. Ну и что с того, что у нас выборка объемом больше 30 наблюдений, что за магическое число такое? \n", - "\n", - "Все правильно, никакой магии не происходит. И совсем скоро мы в этом окончательно разберемся. Как только пройдем тему t - распределения во втором модуле. Вот тут я подробно расписал, как же нам нужно рассчитывать стандартную ошибку среднего, если мы не знаем стандартное отклонение в генеральной совокупности." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Доверительные интервалы для среднего\n", - "\n", - "Если мы имеем некоторую выборку и ГС, то мы **не можем точно** знать среднюю ГС, зная только среднее выборки. Однако **мы можем сказать, с некоторым процентом уверенности**, в каком интервале лежит средняя ГС. Понятно дело, что для нас лучше, чтобы этот интервал был как можно меньше, как это сделать?" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Мы знаем, средняя средних выборок, стремится к средней ГС, также мы знаем, что стандартная ошибка среднего описывает стандартное отклонение распределения средних выборок. Если мы возьмём случайную выборку $X$ и найдём её среднее $\\bar{X}$, а также вычислим стандартную ошибку $se$, то мы можем вычислить доверительный интевал $[\\bar{X} - 1.96*se; \\bar{X} + 1.96*se]$ который описывает среднюю ГС с некотором интервале с 95% доверия.\n", - "\n", - "Загадочное число **1,96** это количество сигм $\\sigma$ в нормальном распределение, необходимые, чтобы охватить **95%** значений в этом распределнии.\n", - "\n", - "" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Если мы рассчитали 95% доверительный интервал для среднего значения, это значит:\n", - "\n", - " - Среднее значение в генеральной совокупности точно принадлежит рассчитанному доверительному интервалу.\n", - " - Мы можем быть на 95% уверены, что среднее значение в генеральной совокупности принадлежит рассчитанному доверительному интервалу.\n", - " - Если многократно повторять эксперимент, для каждой выборки рассчитывать свой доверительный интервал, то в 95 % случаев истинное среднее будет находиться внутри доверительного интервала.\n", - " - Среднее значение в генеральной совокупности точно превышает нижнюю границу 95% доверительного интервала.\n", - " - Если многократно повторять эксперимент, то 95 % выборочных средних значений будут принадлежать рассчитанному нами доверительному интервалу. да-да, тут просто надо представить это в уме\n", - " \n", - " __Если из лекции усвоить разницу между средним ГС и средним выборки, а так же понять, что доверительный интервал строится для выборки, а не для ГС, то ответы в тесте легко определяются.__\n", - " " - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "1.96 sigma\n" - ] - } - ], - "source": [ - "'''Вычисление 1.96 c помощью scipy'''\n", - "from scipy import stats\n", - "\n", - "# 95%\n", - "p = 0.95\n", - "# так как у нас двухсторонний интервал, сделаем вычисление\n", - "alpha = (1-p)/2\n", - "# isf - Inverse survival function (inverse of sf) \n", - "print(f'{stats.norm().isf(alpha):.2f} sigma')" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[8.71; 11.29]\n" - ] - } - ], - "source": [ - "'''Рассчитайте 99% доверительный интервал для следующего примера: \n", - "среднее = 10, стандартное отклонение = 5, размер выборки = 100\n", - "'''\n", - "from numpy import sqrt\n", - "from scipy import stats\n", - "\n", - "p = 0.99\n", - "mean = 10\n", - "std = 5\n", - "n = 100\n", - "\n", - "se = std/sqrt(n)\n", - "alpha = (1-p)/2\n", - "sigma = stats.norm().isf(alpha)\n", - "сonfidence_interval = mean - sigma*se, mean + sigma*se\n", - "print('[%.2f; %.2f]' % сonfidence_interval)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Идея статистического вывода\n", - "### Статистическая проверка гипотез\n", - "\n", - "\n", - "### p-уровень значимости\n", - "\n", - "p-уровень значимости - это вероятность получить такие или более выраженные различия при условии, что в генеральной совокупности никаких различий на самом деле нет.\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "
" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "\n", - "\n", - "# Часть 2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## T-распределение\n", - "\n", - "Распределение Стьюдента по сути представляет собой сумму нескольких нормально распределенных случайных величин. Чем больше величин, тем больше верятность, что их сумма будет иметь нормальное распределение. Таким образом, количество суммируемых величин определяет важнейший параметр формы данного распредения - число степеней свободы." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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///4kJDS+cuyPP/5Iz549sbGxaZWTeS1RDCnUXt6wZilIUwYC843x668G3hdCXG5hWY2m9RIVBffeC5Mnq+2xY1VvYZRx6e6ff4bcc1oCXNMOWbRoETNmzGDXrl107dr4yrG9evViwYIFjB49utG81sASxbAdiDYuL+eAWm1psWkGKWWklDLCuJDLT8C9UspFlpTVaFodlZUwe7YyGwmhTEdRUWfS/f3Vd2Eh3HYb/Otf1pFTYxXmzJlD9+7dmThxIocPH6akpIR33nmHjz/+mHHjxll0jJiYGLp3797Mkp4/jbqrGtcXvR/lbWQLfCqlPCCEmG1Mrzuu0GjZphFdo2kmDh2C77+HceOgIZdAd3dYtAiGnMsKpZqm4IVfD3AwtcEVPc+Z2GAPnpvWs8E8O3fuZP78+ezatQuDwcCAAQO46KKLmD17Nm5ubjzyyCMAjBo1isLCwrPKz507l4kTW/+ChxbNY5BSLkUtam26z6xCkFLe2lhZjaZV07s3xMeDjw8Ax/KO8e2hb6msVssCO9o6clPMTYR5hMH48apMZaVSKL17W0tqTQuwYcMGrrjiClxcXACYPn16vfnaMnrms0ZTQ1wc/PUX3HAD+PggpeTbQ9/y9s63sRE2uDu4A5Bfns8v8b/w+ODHuSLqCuU++MADqpexfz+EmHW80zQhjbXsmxNL3EU7RI9Bo+kQ/Oc/8OOPcNll5DlKntjwBJtSNzEyZCQvjngRX2dfANKL03l649M8t/k51iWv46WRL+H+2GNw6aUQHGzlSmiak9GjR3PrrbfyxBNPYDAY+PXXX/nb3/52Vr623mPQQfQ0mhreew82bKDaw50nNjzB9vTtPDPkGd6f8P5ppQAQ6BrIR5M/4pGBj7A+ZT3PbX4OGRkJ06apwWpNu2XAgAHMnDmTfv36cdVVVzGqxjvtHFm4cCGhoaFs2bKFSy+9lClTpjSxpBdGq1zzeeDAgbI1+vZq2ilSqjECBwcAvjjwBXN3zOXZoc9ybfdrGyz66f5PeXvn2zw37Dmu7nY1fPYZrFoF337bEpJ3KOLi4oiJibG2GK0Cc9dCCLFTSjmwKY6vewwazaJF0KMHJCRwIPsA7/z1DpM6T+Kabtc0WvTWnrcyPHg4r217jYS8BMjPVzOli4qaX26NppnQikGj8fWFQYMoCvLh0fWP4uvsy3PDnrNokNFG2DBn5Bxc7F14ZN0jlN17N6xZA25uLSC4RtM8aMWg0YwaBd9/z/8d+IiTRSd5bdRreDp6Wlzc19mXl0e+THxePJ8e/FyNM+Tlwb59zSayRtOcaMWg6bhIqcYCCgvJKsni+8Pfc1mXyxgQMOCcDzUiZAQTwifw1cGvyC/PVyE07r23GYTWaJofrRg0HZeaOQvffcen+z/FUG3gb33Odj20lHv63kNRZRFfx30NL72k3F81mjaInseg6bgMGABbt5IV6c+PK6/hsi6XEe4Rft6H6+7dnYnhE/n64NfceNXyczJHaTStCd1j0HRchIAhQ/gk6fuGewv7foL/DoS3e6vPvMFwyHyUl9l9Z1NUWcSXB7+ElBR44gkoaNqYPprWw/mG3X722Wfp06cP/fr1Y/LkyaSmtq6g01oxaDomH3wATz1FZlE6Px7+keldp6vYR6ZUGWDlM/DzHeDgAhEj1cfGDubPgj9eObOAj5Hu3t2Z1HkS38R9Q1HSEZg7FzZtasGKaazBuYbdfvTRR9m7dy+7d+/msssu49///ncLSGk52pSk6Zjs3w+HD/PVoW+oklXc1eeu2umlefDDzZC4DgbdBVNeBjs1AY7KUljyMKx7FdJ2w1WfgOMZ99TZfWez6vgqvnI7xD0nT0JAQItVS9P8zJkzhy+//JKwsDD8/PyIiYnh/fffx9bWlvXr1/PHH380egwPD4/Tv4uLi1vdkqVaMWg6JvPmUVFewqKFUxgfPp4w9zq9haWPwPHNMON96H9D7TR7Z5jxHgT3h2WPwapn4bK3Tyd369SNYUHDWBC/kLv7/A1bUB5Qrezhb9MsewLSm9gdOLA3XPxqg1maMuz2008/zZdffomnp6dFyqQl0aYkTcejvByA31PXk1eex1XRV9VOP7IC9v0Iox89WynUIAQMvguG3gs7PoWkjbWSr+p2FenF6WxO3awW/bnrLvPH0bQpTMNue3h4NBh2e/fu3Wd9TCOrzpkzh+TkZG644QbmzZvXUlWwCN1j0HQs8vKgc2d45x1+CtlEsGsww4KHnUkvK4DfHgL/WBj5UOPHG/c0HPoNFj8I92xSvQlgfNh4vJ28+fnoz4zy9ARb2+apT0elkZZ9c9LUYbevv/56Lr30Ul544YUmk/FCsajHIISYKoQ4LISIF0I8YSZ9hhBirxBitxBihxBipElakhBiX01aUwqv0Zwz5eVw662kdw3gz7Q/uSL6CmyEyWOw+nkoTIPp886MKTSEgwtMexdyE2DtmZeVva0907tOZ13yOrKffxRefrnp66JpcUaPHs3ChQspLS2lsLCQX3/91Wy+xnoMR48ePZ138eLF9OjRo0Xkt5RGFYMQwhZ4D7gYiAVmCSFi62RbA/SVUvYDbgc+rpM+TkrZr6ki/2k0501AAPznP3zvdhQbYcPlUZefSTu+BXZ8AkPugdCLLD9mlzHQ/ybY/F9I23N695XRV2KQBhbFL1I70tKapAoa69FUYbefeOIJevXqRZ8+fVi5ciX/aWWTIS0xJQ0G4qWUxwCEEPOBGcDBmgxSStNQkq5A64vlrdGcOgXp6VR2j2JR/CJGhYwi0DXwTPq6V8EtEMY/fe7HnvwSxP0K69+AmV8DEOkZyUUBF7Hg6AJuX5yBzUsvQUYGmHikaNoeTz/9NE8/fR73iAk///xzE0nTPFhiSgoBkk22U4z7aiGEuEIIcQhYguo11CCBlUKInUKIu+s7iRDibqMZakdWVpZl0ms058J330FsLDvWfUN2aXbtQee0vXBsLQydDQ6u535sZy8YdAfE/QY5ZyY4XRV9FcmFyRwY0hlefVV7JmnaBJYoBnN38lk9AinlQillD+By4EWTpBFSygEoU9R9QojR5k4ipfxQSjlQSjnQz8/PArE0mnPkyivhs8+YL3fh5+zHqFATM8CWeeDgBhfddv7HH3w32NrD1vdP75rUeRLuDu5853gQ/v53cHe/gApoNC2DJYohBTB18g4F6p2/LaVcD3QVQvgat1ON35nAQpRpSqNpeQIDKbr+ajae3MiUiCnY2RgtqfkpsP9nGHCzavmfL+6B0Oda2PUNFOcA4GTnxITwCfyR/AcVpUXw22+Qk3PhddFomhFLFMN2IFoIESmEcACuAxabZhBCRAmjD5cQYgDgAOQIIVyFEO7G/a7AZGB/U1ZAo7GIJUvg119Zm/wHFdUVTIkwWWP3zw/UBLQhsy/8PMPuB0OpGsQ2MiViCkWVRexdN1+tC93K7csaTaODz1JKgxDifmAFYAt8KqU8IISYbUz/ALgKuFkIUQmUAjOllFIIEQAsNOoMO+BbKeXyZqqLRlM/b78N+fmseG0o/i7+9PHro/aXFcDOL6Dn5dCp84Wfxz8GoifDtg9h+INg78SQoCF4OHjws0s8A1etgtFmrakaTavBogluUsqlwNI6+z4w+f0a8JqZcseAvhcoo0Zz4SxbRvHxeDZtuYGZ3Weembuw6ysoL1At/aZi+APwxTTY9wMMuBl7G3smhE9g1fFVlM98AUdbC+ZHaDRWRIfE0HQM7O35XcRTWV1Z24y06xsIGQgh575qW71EjALf7urYRmrMSVsT1sI770Ari42jOT/ON+z2jz/+SM+ePbGxsWHHjtrzfl955RWioqLo3r07K1asaC7RG0QrBk3758kn4ZNPWJm0kgCXgDNmpPR9kHkA+l7XtOcTAvrOhOStkJsIwOCgwXg6erI8dQ3MmQNLza/noGmbnGvY7V69erFgwQJG1zErHjx4kPnz53PgwAGWL1/OvffeS1VVVXOJXS9aMWjaN1LC+vVU7NrBptRNTI6YfMaMtGc+2NhDzyub/ry9rwUE7P0B4LQ56Y/U9ZQf3AtvvNH059S0CHPmzKF79+5MnDiRw4cPU1JSwjvvvMPHH3/MuHHjLDpGTEwM3bt3P2v/L7/8wnXXXYejoyORkZFERUWxbdu2pq5Co+ggepr2jRCwaRMrjiyicsvGM2akKoOKoBo9GVx9mv68XmFqUZ+982HMYyAEUzpPYcHRBWwqjWM8QU1/zg7Ea9te41DuoSY9Zg/vHjw++PEG8zRl2G1znDx5kqFDh57eDg0N5eTJk+dZo/NHKwZNh2BVyu8EugbSx9doRkpcC0UZyuTTXPS9Dn65D1K2Q9hgBgUNwsvRi1XHVzH+nd/AxwcuMLSCpmUxDbsNNBh2+3yQ8uxoQtZYxEcrBk37paoKBgyg8p6/scVtC1dEX3HmIdvzPTh5QrepzXf+mOlqpbc98yFsMPY29owOHc26lHVUnwzBxmBovnO3cxpr2TcnTR1225TQ0FCSk89EIEpJSSE4OPj8BL0A9BiDpv1SUACxsRyxO0VZVRljQseo/eVFag2FnleAnWPznd/JA3pcCgcWgKECgNGho8kvz2fXu4/Bu+8237k1zUJThd2uj+nTpzN//nzKy8tJTEzk6NGjDB7c8sEitGLQtF86dYLvvmNBz2pc7FwYFDhI7Y/7FSpLoO+s5peh7ywoPQVHVwIwIngEdjZ2rEtZp9Kt4HGiOX+aKuz2woULCQ0NZcuWLVx66aVMmaLGvnr27Mm1115LbGwsU6dO5b333sPWCos8CXM2LWszcOBAWde3V6M5Z/LzkR4eTPppEr19e/P2OOO6zF9fDdmH4e97mz/aaZUB3uwOkaPhms8AuGvlXWSWZPLLmnDYswfWr29eGdoJcXFxxMTEWFuMVoG5ayGE2NlUa97oHoOmfZKcDN7epH7wOhklGYwONfqLl+VD4jpl/7dQKVQYqllxIJ1fdp/kl90nWXUwA0NVtWVy2Nopc9LRlVBZBsCY0DEcyz9GblQIjBqlXGo1mlaEHnzWtE/s7eGZZ1gfUoY4Jc6E2D66CqoqIGaaRYepMFRz7zc7WR2XWWv/tL7BvDOzH7Y2FiiXmGnw1xdKIXWbwpjQMby2/TWWTgrlxtgbz7VmGk2zo3sMmvZJYCC88AKLbQ7R27c3vs6+an/cr+DqD6GND+hVVlXzwHd/sTouk2cvi+X3h8fw+8NjeGRyN37dk8qjP+6hqtqC1n7kaHBwV+cGwjzC6OLZhbUpa1VvIbXeKPYajVXQikHT/jAYYPt2sooy2J+znzFhRm+kyjKIXw09LgGbhm99Q1U1//h+NysOZPDctFjuGBlJFz83uvi5cf/4aB6e1I0Fu07y5IK9VDemHOwcodtkOLwMqtVg85iwMexM30nFHbfC4MHanKRpVWjFoGl/bNsGgweT8NlcgDNuqsfWQkUR9GjcjPTJxkSW7E3j6UtiuG1E5FnpD0yI5sEJ0fywI4Vvtp1oXKaYaVCSDSe2AjA2dCwGaWDPpJ7w4ovaO0nTqtCKQdP+iI2Fb75hYXg+ga6BdOvUTe0/9Cs4eijTTgMUlFXyf+sSGNfdj7tGd6k330MToxkU0Yl5vx+lrLKRF3vUJLB1VPMngD5+ffB09GRhaB7cdhvY6eE+TetBKwZN+8PLi8qZ17C2aA+jQkapmapVBji0VMVGsmt4PYRPNiSSV1LJw5PPDnJmihCCRyZ3J6OgnK+2HG9YJkc36DpOjTNIiZ2NHSOCR7ApdRPVuTmwdu05VlKjaT4sUgxCiKlCiMNCiHghxBNm0mcIIfYKIXYLIXYIIUZaWlajaVJOnYKvvmJf/AZKDCWMCBmh9p/YAqW5jXojnSqu4JONiVzcK5BeIZ6Nnm5IFx9GRfvyf+sSKCpvJMRFj8sgPxnS9gAwImQEuWW5nHrmYZgyBYqLLaqipm1iaEMhUBpVDEIIW+A94GIgFpglhIitk20N0FdK2Q+4Hfj4HMpqNE3HqlVw880c2fordsKOIYFD1P5DvylTTlTDIQk+WJdAcYWBf07qZvEpH57cndziCj7dmNhwxu6XgLA5bU4aHjwcgDWXRKuFe5ycLD6nxjokJSURExPDXXfdRc+ePZk8eTKlpaXs3r2boUOH0qdPH6644gpOnToFwNixY3nqqacYM2YM//nPfxg7diwPPfQQo0ePJiYmhu3bt3PllVcSHR3NM888Y+XancGSHsNgIF5KeUxKWQHMB2aYZpBSFskzU6hdAWlpWY2mSbn6atixg4WeKfT174ubg5vy+Dm8DLqMVSadesgsKOOLLUlc0S+E6AB3i0/ZL8yLSbEBfLT+GHklFfVndPWB8GFwWC177uvsSw/vHiyzi4fhw8EKoQ/aNGPHwuefq9+VlWr766/VdkmJ2v7+e7Wdn6+2FyxQ29nZarsm1lF6usWnPXr0KPfddx8HDhzAy8uLn3/+mZtvvpnXXnuNvXv30rt3b1544YXT+fPy8li3bh0PP/wwAA4ODqxfv57Zs2czY8YM3nvvPfbv38/nn39OTk7OeV6MpsUSxRACJJtspxj31UIIcYUQ4hCwBNVrsLissfzdRjPUjqysLEtk12jOxsaG7NjOHMw/xIhgoxkp+wjkHVcuow3w2eYkKqskf58Yfc6nfXhyNwrLDXy9tZGxhujJkLEP8lWM/eHBw9mduZviPTvgvffO+byalicyMpJ+/foBcNFFF5GQkEBeXh5jxijvt1tuuYX1JmFOZs6sHdq9JlR379696dmzJ0FBQTg6OtKlS5dakVWtiSWKwdzUzrOcrqWUC6WUPYDLgRfPpayx/IdSyoFSyoF+fn4WiKXR1CEhAZ59lr92GU01IcpUwxHjurnRU+opqOYt/LwzhbHd/Ojs43rOp+4R6MGQSG9+2pliNqb+aboZZTAJqmeQBlJ/+gTuv/+cWq4dnrVr4dZb1W97e7V9o3EmuYuL2q55KXt6qu0rjav1+fqq7WnGMafAQItP6+h4JiKvra0teXl5DeZ3da19P9WUt7GxqXUsGxubVjMOYYliSAHCTLZDgXqnakop1wNdhRC+51pWo7kgduyAV15hV/JWvJ28ifE2Bhk7uhL8Y9WqavWw4Wg2mYXlXDOw/jyNce3AMJJyStiedKr+TH49wDP8tGLo798fZztnfhnlDZmZ5/SC0rQOPD096dSp0+nFeb766qvTvYe2iiWKYTsQLYSIFEI4ANcBi00zCCGihHH1CiHEAMAByLGkrEbTZMycSXVONkuJY1jwMLW2c1m+8kiKbtiM9MOOZHxcHRjfw/+8T39x70DcHO34cUcD5gAhlEnr2FowlGNva8+QwCGsLtyJ9PU973NrrMsXX3zBo48+Sp8+fdi9ezf/+te/rC3SBdHorBoppUEIcT+wArAFPpVSHhBCzDamfwBcBdwshKgESoGZxsFos2WbqS4aDYcMqeSW5Z4ZX0j4A6oNZ0w4ZsgtrmB1XAY3D4vAwe78p/a4ONhxae8gft2byvPTe+LqWM/jFT0Ftn8MSRshagLDQ4azNmUtGct/JPC3dTBvXvOHA9ecFxEREezfv//0ds0azwBbt249K//aOvNTTLfHjh3L2LFj681rTSx6CqSUS6WU3aSUXaWUc4z7PjAqBaSUr0kpe0op+0kph0kpNzZUVqNpcv76C669lr1/LgJgWPAwtf/oSnDyajBo3qJdJ6msklx7AWakGq4dFEpJRRVL9qXVnyliJNg5nTYnjQxW036SdqyEH36AtAbKajQtgJ75rGkfpKTA1q1sKthLjHeMiqZaXa1evlET1LoIZpBS8sOOZPqEetI90HIX1foYEN6JLn6u/LQjpf5MDi4qLMeRFSAlYR5hhLmH8e0gO8jIACus8avRmKIVg6Z9MH06JfFxbKw8fKa3kLYLirMa9EY6kFrAofTCCxp0NkUIwTUXhbEtKZfE7AZmMkdPhlOJkBMPKLfVrTl/USl1ML2GaI0rTrY0LXENtGLQtBt2ZO7EUG04oxiOrAREg7OdF/x1Egc7G6b3abpW+pUDQrARsPCvBnoNNWMeRlfaYUHDKDWUcvzrd2H8eBU6XFMLJycncnJyOrRykFKSk5ODUzPPktchHTVtn9Wr4eGHOfzMJBxtHenv31/tP7oSQgepGcdmkFKyfH8ao6P98HSxbzJxAjycGBzpzbL96fyzvkB8XuHgFwNHV8Dw+xkUNAgbYcORzDiiysuV66o2KdUiNDSUlJQUOvoEWCcnJ0JDQ5v1HFoxaNo+trYQEMCa6sMM8B+Ao60jFGdD6i4Y91S9xfak5JOaX9ZoFNXz4eJeQTy3+ADxmUVE+dcThiN6Ivz5PygvwsPRg14+vfjGt5RLHtnU5PK0B+zt7YmMPHttDE3To01JmrbPuHFkLvqaA2VJZ8xICX8AUg0818Oy/WnY2QgmxgQ0uUhTeqqJasv3N+BhFDVRrT+dpJz4hgYPZX/2fgorCvWKbhqrohWDpm1TUQGVlfyZ9icAQ4OGqv3xq8HFB4L6my2mzEjpDI/ybVIzUg2Bnk4MCPdi2f4GQlyEDwN7FyUrSvZqWc2JeS9BSAiUlja5XBqNJWjFoGnbLFkCnTqRsGkx3k7edPfurtxUE9ZA1/H1ru0cl1bI8ZwSpvZsvhAUU3sFciC1gBM5JeYz2Dkqt1WjYujn1w9nO2f+csqBqVOhoKDZZNNoGkIrBk3bJiICeeutLLU7ypDAISoMRvpe5abagDfS8gPp2AiY3LPpzUg1XNwryHiuRsxJpxIhJwF7W3sGBgzkh6AM+PRTCGg+2TSahtCKQdO26d+fhBf/QVplDkODTcxIoHoM9bB8fxqDIrzxdXOsN8+FEubtQs9gj4bNSTVjIPFrAGVOSipIIq0oTa1Gp9FYAa0YNG2XoiI4fpwtaVsANRcAUC/ZoL7gZj4gXkJWEUcyiri4V/NHMr24VyC7TuSRll/PeIF3F/DuelqZ1QyeZ738NPj7Q2Fhs8uo0dRFKwZN22XJEoiI4OT6X+ns0ZkgtyAVTTX5z4bNSMYW/FSjqac5qTnHigZ7DRMhaQNUlhHlFYWvsy9/dKmCl16CKj0TWtPyaMWgabsMG0bVf97mF5fEM95Ix9aBrGpQMaw8mEHfMC8CPZt/jeUofze6+rmyKi6jgUwTobIETmxBCMHQoKEscE+i+rFHwcur2WXUaOqiFYOm7RIezp6ZoymSZSZmpNXg6KFmPJshs7CMPcl5TIo5/3UXzpWJsQH8eSyXgrJK8xkiRoCtYy231dyyXOLTD8DOnS0mp0ZTg1YMmrZJdjasXMn2xPXYCBsGBg5Uk8Li1ygXUFvzcxP+OJQJwIRmmNRWHxNjAjBUS9YfqSeUg4MrdB5+WjEMCRoCQPGc52DQID0IrWlxtGLQtE2WLYMpU0jesZpY71g8HT0h6zAUpED0pHqLrY7LJMTLmR5NEGLbUgaEd6KTiz1r4jLrzxQ1AbIOQX4Kga6BRHhEsHCgIyxYAM0cME2jqYtFikEIMVUIcVgIES+EeMJM+g1CiL3Gz2YhRF+TtCQhxD4hxG4hxI6mFF7TgbnySsqW/MJStxQzbqrmw2CUVVax4WgWE2L8ES24QpqtjWBcd3/+OJyJoarafKaaMRETt9Xl9glUTrsUnJ1bSFKNRtGoYhBC2ALvARcDscAsIURsnWyJwBgpZR/gReDDOunjjKu7DWwCmTUacHVlWx8vKkXVmYHnhDXg2x28zK+tsDkhm7LK6hY1I9UwISaAvJJK/jqRZz6DXw/wCFF1QMVNKjWUErfHuKqbRtOCWNJjGAzESymPSSkrgPnADNMMUsrNUsoaQ+hWoHljwmo6NidPwrvvsmf/KhxtHenn3w8qSiBpU4PeSKvjMnF1sGVoF++Wk9XI6G6+2NsK1tTnnSSEMiclrIUqA4MCVRjuks/+BzNnQgcPNa1pWSxRDCFAssl2inFffdwBLDPZlsBKIcROIcTd9RUSQtwthNghhNjR0eOtaxph/Xr4+985Gr+F/v79VZjt45ugqrzeaKpSSn6Py2RUtB+OdrYtLDC4O9kzJNKH1Q25rXadAOX5cHIHHg4e9PTpyTdDHSAuDnx9W05YTYfHEsVgzhhrNiawEGIcSjE8brJ7hJRyAMoUdZ8QYrS5slLKD6WUA6WUA/38/CwQS9NhmTWL3EN/8Ydbukk01TVg56S8e8xwILWA9IIyJrSgm2pdJsT4k5BVTFJ9S352GQvCttY4w4aqeIq6hKoehUbTQliiGFIAU6NtKJBaN5MQog/wMTBDSplTs19KmWr8zgQWokxTGs0FscU+FYyTwQA18BwxEuzND9SujstACBjXw3qKoWbdh3p7Dc5eav6FidtqlaziyIqv4dVXW0hKjcYyxbAdiBZCRAohHIDrgMWmGYQQ4cAC4CYp5RGT/a5CCPea38BkYH9TCa/pgCQmwn33cWTHMjwcPOjh3QNOJUHO0QbHF9bEZdI/zKtZg+Y1Rpi3C90C3Bp3W03dBcXZ9PPvh6OtI/krF8Pzz+v5DJoWo1HFIKU0APcDK4A44Acp5QEhxGwhxGxjtn8BPsD7ddxSA4CNQog9wDZgiZRyeZPXQtNxiItDfvEF+9J2MSRoCLY2Z0wv9SmGjIIy9p3Mt4o3Ul0mxASwPSmX/NJ6ZkFHTQAkJPyBo60jA/wH8NFwG6UUOnVqUVk1HReL5jFIKZdKKbtJKbtKKecY930gpfzA+PtOKWUno0vqabdUoydTX+OnZ01Zjea8ueQSThzfzXbPfIYEqhnCJPwOnuHgE2W2yJnZztYzI9UwoYc/hmrJhqP1OFgE9Vcrz5m4re6rOE429YxLaDTNgJ75rGlzbMnaAUKoENWGChU4L2pCvQO0aw6p2c7dA1putnN99DfOgv69PnOSjQ10GafGGaqrT4+hHPvyHbi7Xqc+jaZJ0YpB03Y4fBgmTiR5w68EuwYT5h4GyVuhorDeMBhllVVsPJrd4rOd68N0FnRVtVnnPlWX4ixI30MP7x54OXqRvW8rrF2rl/vUtAhaMWjaDllZyKwsthXFMSx4mHrRH10FNvYqcJ4ZthzLobSyivFW9Eaqy/gYf06VVLLrRD2DyTUhPY6uxkbYMCRoCG+NqkYePgweHi0nqKbDohWDpu0wciT7Vn/FIe/K2m6qnYeBo3kz0e9xmTjb2zK0i08LCtowo7v5YWcjWHOoHnOSmx8E94f4VYCaz5BRlkVifmILSqnpyGjFoGkbSAlSsjVtKwCDgwZDfgpkHoQo82YkKSW/H8pkZLQvTvYtP9u5Pjyc7Bkc6V3/OAOoOqVsh5Lc00ow652XYGL9LrkaTVOhFYOmbbB/P4SHk71yETHeMXg7eSszEkD0ZLNFDqUXcjKvlAmtyIxUw/ge/hzOKCQ5t8R8hujJIKsh4XdC3UMJcw8jvui4irRaUk8ZjaaJ0IpB0zaQEsOQwWywPV7bjOQZBn7dzRb53WiqaU3jCzXUzIL+vT5zUsgAcPautarbfwcUU/nLAnBxaSkxNR0UrRg0bYM+fdj6n4dI8bZRisFQAcfWqklt9XgbrY7LoHeIJ/4erW+hmwhfV7r4udYfHsPGFrqOr+W2WlxZzIHsA1BV1bLCajocWjFoWj9VVVBQwJbULTjYODAgYACc2AIVRfW6qWYWlrE7OY9Jsdaf7Vwfk2IC2Hosh8L61oKucVtN282QoCEIBBXPPQvduqkxF42mmdCKQdP62bULvL0p/20R/f3742TnpDx2GnBT/T0uEynPmGxaIxNjA6iskqyrby3oGrfV+NV4OnoS6xPLVt8iuOIKKC9vOUE1HQ6tGDStH19fSh75O6t9cs8s43m0YTfV1XEZhHg5ExNk/dnO9TEgvBPerg6sPliPOanGbfXoGbfVz6LzKHr5eb0OtKZZ0YpB0/qJiGDNXWPJ8bRTYTDyTkBWXL3eSCUVBjYczWZSbECrmO1cH7Y2gvE9/Pn9UCaV9a0FHT0ZTu6A4hyGBw/HIA1sT9sGaWktK6ymQ6EVg6Z1U1kJu3axJWUTnRw7EeMdA0dWqLRuF5stsvFoNuWG6lY9vlDDpNgACsoMbE/KNZ+h21Tlthq/in7+/XC2c8bt4aegTx+orkeZaDQXiFYMmtbNtm0wYAA2i39jaPBQbIQNHFkO3l3B13w01VUHM3B3smNwZMuv7XyujIr2xdHOhlX1mZOC+oFbABxZjoOtA4MCB/FjXwEvvwwGQ4vKquk4aMWgad3ExJD6wRv80bWaEcEjoLwIEterlrQZqqrVbOdx3f2xt239t7eLgx0jo3xZdTADac7TyMZGmZPi14ChguHBw1kWXkTydVPBwaHlBdZ0CFr/k6Pp2Hh7s3yENwWutmp84dhaqKqA7uYVw64Tp8gprmgTZqQaJsYGkHKqlMMZheYzdL8YygvgxBaGB6s1rXfErYI//2xBKTUdCYsUgxBiqhDisBAiXgjxhJn0G4QQe42fzUKIvpaW1WjqpawM5s9nz6E/iO4Ujb+LPxxZBo6eED7MbJFVBzOwtxWM6e7XwsKePzULCK06UI85qctYsHWEI8uJ8Igg2DWYgH+/DVOm6MlummahUcUghLAF3gMuBmKBWUKI2DrZEoExUso+wIvAh+dQVqMxz6ZNMGsWcstmhgcNV4OtR1aqRXls7c/KLqVk1cEMhnbxwcPp7PTWir+7E/3CvFhZ3ziDg6uar3F4GQIYFjyM90faYPhlYYvKqek4WNJjGAzEG5fprADmAzNMM0gpN0spa4LLbwVCLS2r0dTL2LHs+vV/bOnuxPCQ4ZC2C4oz6x1fOJJRxLHsYqb0DGxhQS+cqb0C2Xcyn5RT9QTI6zYFTiVCTjwjQkawJ6iafTFeYNt6osZq2g+WKIYQINlkO8W4rz7uAJada1khxN1CiB1CiB1ZWfXMBNV0LGxtWel/CunizAD/AXB4OQibesNgLN2XhhAwuWfbGV+o4eJeSpkt359uPkONMjy8jMGBg7ERNhza8DN8+20LSajpSFiiGMzNEDIbqEUIMQ6lGB4/17JSyg+llAOllAP9/NqOfVjTTJw6Bc8/T/yuVQwMGKjCYBxZDmFDwMW8G+ry/ekMivDG373tzQru7ONKbJAHy+pTDF5hENALjqzA09GT3r698fz6Z7jjDh0eQ9PkWKIYUoAwk+1QILVuJiFEH+BjYIaUMudcymo0Z7FzJ/Lf/6Ys+ZjyRspPgfS9yqRihoSsIg5nFJ5uebdFLukdyM7jp0jPLzOfodtUFTywJJfhwcN5a6yg4NAecHRsWUE17R5LFMN2IFoIESmEcACuAxabZhBChAMLgJuklEfOpaxGY5aJE/nlz0/Y18WFUSGj4NAStb/HNLPZa0wwU9uwYpjaKwiAFQfq6TX0uBRkFRxZzsiQkWR42bKpOqEFJdR0FBpVDFJKA3A/sAKIA36QUh4QQswWQsw2ZvsX4AO8L4TYLYTY0VDZZqiHph3ye+EuAjxCiPSMhLhfwa9HvbOdl+5Lo3+4F0Gezi0sZdMR5e9GtwA3lu6rJw5ScH/wCIW43+jp05NOjp1I/eUreP75FpVT0/6xaB6DlHKplLKblLKrlHKOcd8HUsoPjL/vlFJ2klL2M34GNlRWo2mQ5GSqrptJ1rY/GBU6ClGSC8c3Q4/LzGY/kVPCgdQCLjG2uNsyU3sFsT0pl6xCM+MGQqheQ8IabA1lylNr0ybke+/p5T41TYqe+axpfSQmUvXHGsqqypQZ6cgyZUKJMa8Ylu1XLey2bEaq4ZLegVRLWHmwHnNSzGVgKIP41YwKGcUHk9zYv2+VXu5T06RoxaBpfYwezX9+fYwTYe4MChwEcb+ptZ2D+pnNvmx/Or1DPAnzbvsvx+4B7nTxdWXZvnoUQ/hwtRZ03G+MCB5BuaMtG9I3t6yQmnaPVgyaVsmG1I0MDBqES3U1JPyuTChm1lY4kVPC7uQ8Lund9s1IAEIILukdxOaEbPPmJFs7FTvpyAq87Fzo49eH6m++hpkzW15YTbtFKwZN62L/fir69cZl1wFlRopfDVXl9Y4vLN5zEoBpfduHYgCY0S+YaglL9tbj2d3jMijPh6QNjAoZRUF6EpWJCVBU1LKCatotWjFoWhfFxZxyqCLb045RoaPg0G/KdGImaJ6UkkW7Uxkc4U1op7ZvRqohOsCd2CAPFu2uRzF0HQf2rnDoN0aFjuK7Cd4s/+45cHNrWUE17RatGDStiyFD+Pcr43CMiKKzS5AKmtf9EmVCqcPBtALiM4uY0T/YCoI2LzP6BbM7OY/jOcVnJ9o7q0CCh5bQw6sbPs6+bEjZAObWc9BozgOtGDStB4OBstJCtqVtY2TISDj2hzKZxJif1PbL7lTsbES7cFOty/R+wQih6miW2BlQlIFNirpWPl/9jOzWTa/qpmkStGLQtB5Wr8YuIIiIY6eUGWn/AnDyhK7jz8paXS1ZvDuVsd396OTa/lYyC/J0ZnCEN4t2nzS/slu3qWDnDPsXMCp0FEmeVeT27w75+S0vrKbdoRWDpvUQGMjuCT3ICOvEYJ8+KgxGzDSwO/vF/2diLukFZUzv11Cg37bN5f1DOJZVzIHUgrMTHd2g22Q4uIgRAUPY2q8Tnz06Fnx8WlxOTftDKwZNq6G6bx8em+XBwMhROCSug4pC6HWV2by/7D6Ji4Mtk2LaXohtS7m4VyD2toJFu06az9DrKijOwi1tN0MCh/BH8h/I3NyWFVLTLtGKQdM6yMvjyO7VZJVmMS5snDIjufhCxOizspZVVrF0XxpTegbi7NB+F6rxcnFgbHd/Fu9JxVBVfXaG6Mng4Ab7FzA2bCxDf9kF/v6Qk3N2Xo3mHNCKQdM6+PFHegyYQmSGgdH+F6m1F2JnmPVGWnEgnYIyA1dfFGrmQO2LqwaEkllYzvqjZhavsndWHltxixkbPJK/urmy897pLS+kpt2hFYOmdTBxIh/e3QffPkPxPL4FKkug15Vms36/PZkwb2eGdWn/9vQJMf74ujkwf1uy+Qy9roTSUwRmxOHQdwDvTHXR4wyaC0YrBk2rINnXjv8Or2Zc+HhlRnIPMjup7XhOMZsTcpg5MAwbG3MLBLYv7G1tuOqiUNYcyiSz0MwCPl3HK8+t/T8zNmwsB9P2kPfHUj2nQXNBaMWgsT7HjnHoh3nYGSRj/QfC0VUQeznYnD1+8OOOFGwEXH1R2NnHaadcOzCMqmrJgr/MDELbOarFiw4tYXzQCC7dfAqv8ZfC/v0tL6im3WCRYhBCTBVCHBZCxAshnjCT3kMIsUUIUS6EeKROWpIQYp/pAj4aTS0+/ZTxd79BT6fOhJ3YoWIjmfFGMlRV8+POZMZ29yfQs+2t63y+dPVzY3CEN99vTzY/p6H3VVBeQLfMBA4Pj+Ljf02FLl1aXlBNu6FRxSCEsAXeAy4GYoFZQojYOtlygQeBufUcZlzdBXw0mhry/3kvdzzZhcExU2DPd+ATDaFn3yrrjmSRUVDOzEEdp7dQw8xBYSRmF7Mt0Yw7auQYcA9G7PmO/r2m8EF0FqWO2higOX8suXsGA/FSymNSygpgPjDDNIOUMlNKuR2obAYZNe2cdad2sDPamXGe3eH4Jug3y2yI7fnbk/F1c2R8D38rSGldLukdhLujHd9vNzMIbWMLfWdC/GrG+fXHMb+YxDefBj2nQXOeWKIYQgDTuzHFuM9SJLBSCLFTCHF3fZmEEHcLIXYIIXZkZZlxzdO0T5Yto/Q/bxLiFECv4zsBAX2uOytben4Zvx/K5KoBIdjbdrzWsLODLdP7BbNkXxp5JRVnZ+h7PcgqBqYdoecpR2KfeBvWrGl5QTXtAkueMHOuH+fi8jBCSjkAZYq6Twhx9owlQEr5oZRyoJRyoJ+f3zkcXtOWqfhxPsO/38qEiEmIvfOhy1jwPLvd8dXWJKql5IYhnVteyFbCTcM6U26o5jtzrqt+3SBkIHZ75hMyZjrXv9KLssvNr2Gh0TSGJYohBTA16oYC9YR8PBspZarxOxNYiDJNaTQArHjqKmb9qwuTnYMg7zj0u/6sPGWVVXz75wkmxgQQ7tN+1l04V3oEejCsiw9fbUkyPxO63yzIPMAkr27sC4JNaXrJT835YYli2A5ECyEihRAOwHXAYksOLoRwFUK41/wGJgPaj05zmpXHV+EcEEqfhK3g4G52pbbFu1M5VVLJbSMiWl7AVsZtIyJIzS9j5cGMsxN7Xgm2DgxK3kPnchfsHn8SdmhHQM2506hikFIagPuBFUAc8IOU8oAQYrYQYjaAECJQCJEC/BN4RgiRIoTwAAKAjUKIPcA2YImUcnlzVUbTtih/4Vn6/edHJoWORcT9Aj0vB4faPQIpJZ9uSqRHoHuHmOncGBNiAgjzduazTYlnJ7p4Q/dLsN//M8M7j2bQwp1Ubt/a8kJq2jxnB6Ixg5RyKbC0zr4PTH6no0xMdSkA+l6IgJr2S3rcNgKzyrjIYA8VRWbNSFuP5XIovZDXruqNMOOp1NGwtRHcMiyCl5bEsf9kPr1CPGtn6HcDHFzEGHd/Rv23B3On9GScdUTVtGE6nnuHptUw9+5uvP3QRfSJWwZ+PcyGwPhsUyKdXOyZ0Y7XXThXrh0UhouDLZ+a6zVETQDPMAYfXY+Tmxcrj69seQE1bR6tGDRWoaisgM0nNzPJrz82J/+CgbefNXfheE4xq+MymDU4HCf79hte+1zxcLLn6otC+W1PGhkFdeIn2djCRbdgn7ieyV79mPrQ/zC8P886gmraLFoxaKxC5dBB3Df/BJNPZYK9C/SZeVae/1ubgJ2tDbcOj2h5AVs5d47sQpWUfLT+2NmJ/W8GGzvGV5RhU1lJQs6RlhdQ06bRikHT8hgMbI92IjfCn75xq1RcJGevWllO5pXy818pXDcoDH+PjhMXyVLCfVyY0TeYb/48QU5Ree1E9wDocRlD41bzzJP9+d8oi4YSNZrTaMWgaXGyKk7x6DRwuHgwNpUlMOiOs/J8uC4BKeFvY7paQcK2wb3julJmqDI/1jDoDuzL8pjq3oV1yesoOJXW8gJq2ixaMWhanA3rPqe6uoppx/dB8AAI7l8rPbOwjO+2J3PVgFBCvJytJGXrJ8rfnUt6BfHF5uPkl9QJUxYxCny7MS3tGG/PPULJjEusI6SmTaIVg6ZlSUvj8ksf45H1ksiso2Z7Cx9vSMRQVc09Y3VvoTHuGxdFUbmBL7Yk1U4QAgbeTs+UPewZFsbyftocp7EcrRg0LUpCRRov3RSMV89O4OytZuuakFtcwddbjzO9bzARvq5WkrLtEBvswcQYfz7dlEhRuaF2Yt9ZCAc3HMZE8OZFRZwsMrPQj0ZjBq0YNC3K4ux1LJjgy8jiAzD4rrNmOs/7PZ6yyiruHx9lJQnbHg9OiCavpJIP63ooOXvBgJu57NgOHCuq2f7Le1aRT9P20IpB02JUn8ol/7vPGFvlgY+NAwy6q1b6iZwSvtqaxLUDw4jyd7eSlG2PPqFeXNoniI/WHyOz7ryGofcQYjDw8k95XHz7a8jiYusIqWlTaMWgaTGOffMuz7+5j5m7j0DfWeBWO7z63JWHsbURPDSpm5UkbLs8Ork7lVXVvLPmaO0Er3DoeQWyv+CBB8M4WBhvHQE1bQqtGDQtxiexxdz/RBT9O5XDsPtqpe1NyWPxnlTuHNmFAD1v4ZyJ8HXlxqGd+X57MvGZRbUThz/AMJci/urtxYJEiwIjazo4WjFoWoRTZadYcXINIWE2OHW/BHyjT6dJKXl12SG8XR342xi9iP358sD4KJztbXl9+aHaCcH98Og8iiszSvF69yNKctKtI6CmzaAVg6ZF2PN/z3Ljb6lcnZ0Nwx+olfb7oUw2J+TwwPgo3J3srSRh28fHzZG/je7CyoMZbD2WUztx+INcnZDBA/OT2fXjO1aRT9N20IpB0+xIKSld/itXb8ojOmwIhA89nVZaUcVziw8Q5e/WoZftbCruHNWF0E7OPLNoPxUGk1XeoiYS3a8X97wSzX9DzMyU1mhM0IpB0+zsyNjBY9d7sPdeLxj3VK0oqvP+OErKqVJeurwXDnb6drxQnB1seWF6T+Izi/h4o4n7qhCIcc8w0qGYA7kHOZhz0HpCalo9Fj2JQoipQojDQoh4IcQTZtJ7CCG2CCHKhRCPnEtZTfvnx0Pzca+WTAy5CCJGnt4fn1nIh+uPceWAEIbq1dmajAkxAUyODeDdNUdJzi05k9BtCtMcu/DCZyc58vZT1hNQ0+ppVDEIIWyB94CLgVhglhAitk62XOBBYO55lNW0Y06VnWLm7P/x0i+pOI195vR+KSXPLNqPi4MdT10SY0UJ2yfPTe+JQPDCrwfO7BQCj8nPMfB4CRlx2yiu1HMaNOaxpMcwGIiXUh6TUlYA84EZphmklJlSyu1A5bmW1bRvftvzNanedvT0CYHOZ1Zo+3FnCluP5fLY1O74ujlaUcL2SYiXM/+YGM3quEyW7jOJrBo1gdynBzFvug9Lji6ymnya1o0liiEESDbZTjHuswSLywoh7hZC7BBC7MjKyrLw8JrWTGV1JV8e/ZqFN/sR8Pwnp/cn55bw718PMiTSm1mDwq0oYfvm9pGR9An15OmF+87MiBaCvmOfJ6a8gu+3v0e1rG74IJoOiSWKwdwK7NLC41tcVkr5oZRyoJRyoJ+fn7ksmjbG6n3zkVn53OLeHcIGA1BdLXnkxz0AzL2mLzY25m4RTVNgb2vDW9f2paSiiicW7ENK9eiJruN5+dcy3n5sJxvjl1pZSk1rxBLFkAKEmWyHAqkWHv9CymraMFJKDn72EisePswo31tP7/90UyJ/Jubyr2mxhHm71H8ATZMQ5e/O41N78PuhTOZvN3behSDi6n+ydog73256zboCalolliiG7UC0ECJSCOEAXAdYOq/+Qspq2jA7D/7AsnA4OKsPNhMuB+BweiGvrzjMpNgArrko1LoCdiBuHR7BiCgfXvztIEnZasDZ7pa/U3XjCDaJPOISVlpZQk1ro1HFIKU0APcDK4A44Acp5QEhxGwhxGwAIUSgECIF+CfwjBAiRQjhUV/Z5qqMppUgJV9sf5PyTvZEfbAC7OwoLKvknm924uFkzytX9kYIbUJqKWxsBG9c3Rd7Wxvu/eYvyiqrALhqwlsMPVzMjyuftbKEmtaGRfMYpJRLpZTdpJRdpZRzjPs+kFJ+YPydLqUMlVJ6SCm9jL8L6iurad8k7focdmfw95xInN0DkVLy2E97OZ5TwnvX99deSFYg2MuZd2b2Iy69gGcW7UdKiUdmBR+9kojzhhNkxC2ytoiaVoSeaqppWsoL+WL7XP7+UwbTlxYA8NGGYyzbn84TU3swRE9ksxrjevjzwPhoftqZwnfbkiEmhuwv3+fn0Z34asNzUFnW+EE0HQKtGDRNysmVT7DIUbDg/Vtx+OhTNidk89ryw1zcK5A7R0VaW7wOz98nRDO6mx/PLz7A7uQ8fG+6h3HhQ/je3kD2H/+2tniaVoJWDJqmI3kbHx1fihA23DzheeLd/Zn91U4ifFx4/eo+elyhFWBrI/jPzH4EeDpy5xfbSc4t4aFTw7hpSTafHf4O0vdbW0RNK0ArBk3TYKgg5df72Fliz4J3C7E/kMotn27Hwc6Wz28brMNptyI6uTrw2a2DqayS3PLZNjw37WHmjip+dnYhe/F9UF1lbRE1VkYrBk3TsOFNPqzOJvhUNSF58NDKE+QWV/DprQP1fIVWSJS/Gx/dPJCU3FLu7HYlBdu3UmZvyydlSbD1fWuLp7EyWjFoLpwTf5K8+S0Wu7sRPuMObn/yOzYW2zPv+v70CfWytnSaehgc6c3ca/uyIb2MN5blcVnny1jg6kHm2pcgfZ+1xdNYEa0YNBdGWT4suJP3/QIJzZUc3N+fjQk5vHZVHybEBFhbOk0jTO8bzAvTe7Jr2yEevPYzLtuYx4fePvDTHVBR0vgBNO0SO2sLoGnDSAm//ZN9pZks8/BjxZxkNgTNZdonn3LNwLDGy2taBbcMj6DSUMWaDX0o9ndluXMC16UcI2rFUzDtHWuLp7ECusegOX/2fIfc/xOvRsRiJz2YM+J2PO65i+sG64ipbY07R3el4N33+d7uOgROvN6lD3LnZ3BQR7DpiOgeg+b8SN0Nv/2T38L7sbcim7Ksqxjy1G1M1us2t1n+NqYr9hXl7P0skDVTjrE2OJZxi+4Fv+7qo+kw6B6D5twpyoT511Pk7M2/MDB4lxM/lblxw0WWLtOhaa3cHr+Od75bTI8jTjxq50i5nSN8NwtKT1lbNE0LohWD5twwVMD3N1FdnMMV9sMw2Bbw5DEf+n7zP2tLpmkKbrsNNmxg9LRnKbfN4WqnCci8E2owWs9v6DBoxaCxHClhyT8heSt3y+tI99jJ8MAJRP2yDNatAzttmWzzODnByJHcP2Qafb2HkOS+k4eZCQlrYOUzjZfXtAu0YtBYjGH1i7DrK94xzGBvWCJe9q7MGfhPEAKCg60tnqYJEe+/z8fvHcfZ3paNoZl8YpgCW9+nasPb1hZN0wJoxaCxiJxVb2G36U2+NYxnW++elNok8k7eaHx7DobDh60tnqapsbXFydmNJ2Lvp9T2EL/3HM4vVcOxXfM8uRs+srZ0mmZGKwZNg0gp2bZoHj6bXmAVQ5CXP8mRyh8ZGzqWAcOvhcmTISrK2mJqmpq//Q0WLuTy/jcyKHAQx+T3FFz2bzbIfniueZQdSz+3toSaZsQixSCEmCqEOCyEiBdCPGEmXQgh3jWm7xVCDDBJSxJC7BNC7BZC7GhK4TXNS2peKZ/Me4mLdj3DPod+xNz3LSuy5uFg48AzQ59B9O8PX34JtrbWFlXT1Bgj4dpkZPKqYSqGagObCj4hfPaPHLHrQd8//8mH//cmmYV6DYf2SKOKQQhhC7wHXAzEArOEELF1sl0MRBs/dwP/Vyd9nJSyn5Ry4IWLrGluqqolX289zidvP82dOXNJ9x1K7MNL+enE1+zK3MULXe8h4NV5UFRkbVE1zc0dd+B/90M81u8hNqVuYlX2YqL/uZxsr97ckf4i7775b37amYKU0tqSapoQS3oMg4F4KeUxKWUFMB+YUSfPDOBLqdgKeAkhgppYVk0L8NeJU1w+byMnfn2FZ8UnlEROIeSeX9iUtZNP9n/C1d2uZtK+cnj9dUhLs7a4mubmrbdg7Vqu7jmLiyMu5r+7/suugqME3beU8rARvMR77F4wl6s/2ML+k/nWllbTRFiiGEKAZJPtFOM+S/NIYKUQYqcQ4u76TiKEuFsIsUMIsSMrK8sCsTRNycm8Uv75w26ueX8Dt+T9l6fsv0P2vAKXG78hrSyXpzY+RfdO3Xl80ONw552QkADR0dYWW9PcdO8O0dEIIXhu8NOEu4fz+PrHya4qxeWWn5HRU3jJ/jOmZ37AjHnreXLBPjILtHmprWOJYjC37FbdfmNDeUZIKQegzE33CSFGmzuJlPJDKeVAKeVAPz8/C8TSNAW5xRW8+NtBxr2xlnV741kVMI+rq1fA8AcRV31Kmazi4XUPY6g28OaIV3FKSlEFQ0OtK7imZXn8cVwvuZy5o16noKKAx9Y/RqWNLeK6b2HgHdwif2GJ///4bcdRRr/xB68vP0R+aaW1pdacJ5YohhTANFRmKJBqaR4pZc13JrAQZZrSWJnsonJeXXaI0a//wWebErk7poKt/q/SpXAnTP8vTH6RKiRPbniS/dn7mTNiDp3/9wP06QOJidYWX9PSxMZC//509+jKc8OeY3v6dp7f8jzSxhYufROmvkaPgk3sDJ7L9dFVvL82gVGv/c5bq45wqrjC2tJrzhFLpqpuB6KFEJHASeA64Po6eRYD9wsh5gNDgHwpZZoQwhWwkVIWGn9PBvSK41YkObeETzYmMn/7CcoN1VzaO4hnQ3cTsOFpsHeBmxZCpOrUvbnzTVafWM1jgx5jQucJcFssuLhAZKSVa6FpcW655fTPaV2nkVKUwvu73yfYLZj7+t0HQ2eDdxccFtzJvwrv4bbLXuOlxG68u+YoH284xo1DO3Pr8AiCvZytWAmNpTSqGKSUBiHE/cAKwBb4VEp5QAgx25j+AbAUuASIB0qA24zFA4CFxkXg7YBvpZTLm7wWmgaRUvJnYi6fbUpk1cEMbITgiv4h3Dvcn8ht/4bfv4WIUXDlR+ChfAa+Pvg1Xx38ihtjbuSmbrNUOIygIPjHP6xbGY11OXAA5s5l9v/+R2pRKh/s+YAg1yCujL4Suk2G2Rvhp9sJW30P/xt4O0fue4L3NqXy8YZjfLIxkam9Arl9RCQDwr0wvhc0rRDRGt3MBg4cKHfs0FMeLpRTxRUs2HWS77adID6zCC8Xe24YEs5NQyMIzNoIi/8Ohakw6hEY+wTYqPkIPxz+gRe3vsiE8Am8OeZNbP/5sPJA+vZbPWeho7NwIdx9N6xdS2VMN+5fcz9b07by0oiXmNZ1mspTVQlrXoDN/4VOETB9HileF/HlluN8t+0EhWUGYoI8uH5wGDP6h+DhZG/VKrUXhBA7m2pKgFYM7YwKQzXrjmSxaNdJVsVlUGGopl+YF7MGhzG9bwjOlXmw6l+w+2vw7Q6Xvw+hZ+6lb+O+5ZVtrzAmdAxvjX0LB1sHeOMNSE2Ft3WcHA1QUAAeHgCUVJbw4O8Psi19Gy8Mf4Eroq84ky9pI/xyP5xKhIF3wIR/UWzjxkJjY+VAagFO9jZMjg3kigEhjIryxc5WB2M4X7Ri0NTCUFXN1mO5LNmXxvL9aZwqqcTH1YFpfYOZOSiMmCAPqDLAjk/hj5egvAhGPAhjngB7p9PH+eLAF8zdMZcJ4RN4Y/Qb2NvYnZ4Bi5Rnfms0AB9/DMOHU9otkn/88Q82p27mX8P+xTXdrjmTp6IYfn8Jtv4fuHjDhOeg/41gY8u+lHzmbz/Bb3vTyC+txNfNgYt7BXFpnyAGRXhja6Pvt3NBKwYNJRUGNhzNZvXBDNYcyiS3uAIXB1smxARwRf9gRkX7YW9ro17oR1aorn3mQYgcA1NfhYAzk9cN1Qbe3PEmX8d9zaTOk3ht9GvYZ+bAFVfAvHlw0UVWrKmmVZKXBz16qHvk//6P8qpyHvrjITac3MBdve/i/v73YyNMWv+pu2HZ45C8FYL6wsTnocs4EIJyQxVrD6te7h+HMymrrMbXzZFJsf5MjAlgRJQvTvbahNkYWjF0QKSUxGcWse5IFuuOZPFnYi4VhmrcnewY192fS3oHMba735kHSEpIXKdaaynbla130osQM61Wy7+wopDH1j/GxpMbuTHmRh4Z+Ai2NrZw8CBccw188w3062eVOmtaOceOQefOp8edKqsqmfPnHH4++jMTwycyZ+QcXOxdzuSXEvb/DKueg4IU6DwSxj8DnYedzlJcbuCPw5ks25fOuiNZFJUbcLK3YVgXH0Z382NMNz8ifV31wLUZtGLoAEgpSc4tZWtiDlsSctickE1GQTkAXf1cGdPNn4mx/gyK8FY9gxqqq+DQEtj8rlIIHiEw+lHVfbetPcgXfyqeR9Y9wvGC4zw19CllAjAYziy4U1WlB5s1jVNQAK+8As8/j3Rw4KuDXzF3x1x6ePfgjTFv0NmjzjrghnLY+TmsnwvFmdB5BAx/EKIng82Ze7nCUM2fiTmsPpjBuiNZJOWUABDi5czQLj4M7+rDkC7ehHZyQaMVQ7uk3FDFwdQCdp3IY+fxU2xPyiWzUCkCXzcHhnbxYUSUL6O7+RFizhe8NA/2fg9//g9yE1QPYdj90P+mWuMIoJTOd4e+462db+Fq78rro19nSNAQKC2FadNgwgR48snmr7SmfbBgAVx3HaxZA6NGAbA+ZT1PbniSyupKnhz8JJdHXX52K7+iBHZ+BlveVz0Ivx4w+C7oMxMc3c86zYmcEtYdzWJLQjZbj+WSa5w4F+zpxMAIby7q3In+4V70CPTAwa7jDWJrxdDGqTBUE59ZxP7UfPal5LP3ZD5xqQVUVFUD6kYfFOnNoAhvBkd6E+3vZr7rLCUk/wm7voJ9P4OhFEIuUgohZjrYnj1NJb04nRe3vsj6lPWMDBnJiyNexNfZVyUaDHDHHUox3Hxzc14CTXvj+HFlVoLTjgrpxek8tfEptqdvZ1LnSTw15Kkz95opVZWwfwFsmQfpe8HBDXpfo3q5IReZdXqorpYczihke1Iu2xJz2Z6Ue7pH7WhnQ89gD/qEetErxJPeIZ508XOt3bNuh2jF0EaQUpJRUM7hjEIOpxdwOL2IuLQCjmYWUlmlrrubox09gz3oG+bFgHAv+oV1ItDTqaGDQtZhZavd+z3kHVczlntfAwNvh+B+ZotVVlfy9cGv+b89/0e1rOahix7i+h7XK4Vz/Lha6zcgQHsfaS6M9evhqafgp58gMJCq6io+O/AZ7+1+DydbJx7o/wAzu89U41h1kRJO7lTec/t/BkMZeHdVPYheV4Fv/QtCSSlJzS9j94k8/jpxin0p+exPzaekogoABzsbugW4ERPoQfdAd/UJcMfP3bHdjFdoxdDKKK2o4nhuMUnZxSRkFZOYXUx8ZhEJmUUUlhtO5/NzdyQmyIPYIA9igtzpFeJJpI8rNo255VVXQeouOLwUDi6GnKMgbJSHUZ+ZEHOZ2a43qAdmXco63tn5Dgn5CYwNHcvjgx8n1N0YBK+iQkXQjI2FJUua6pJoOipLlsDzz8OqVeDldXp3Un4SL//5MlvSthDjHcM/BvyDYcHD6n8pl+XDwV9g7w+QtEHt849VzhPdL4bAvrXGI8xRVS05llXEgdQC4tIKOJimvrOLzsRucneyI9rfjSh/NyJ93eji50qkryvh3i5tzhNKK4YWpqpakl5QxslTpaScKiE5t5TkUyWcyC3hRE4J6XXCDPu7OxJlvNmi/N3oFqBaJ51cHSw/af5J9UDEr4GENVCSA8IWIkaqhyNmGrgH1ltcSsmW1C3M2z2Pfdn7CHMP47FBjzE2bKzKUF195sFasgS6dlXuhxrNhVJzbxkMMH8+XH892NggpWTl8ZW8ueNN0orTGOA/gPv738+gwEENHy8/BeJ+g7hf4cRmkNXg6g9RE6HreIgc1eCzUJecItWLP5JeSHxWEfGZRcRnFpNdVH46jxAQ5OFEuI8LYZ1cCPd2IczbhdBOzoR0csbf3anVzbPQiqEJKTdUkVVYTkZBOZkFZaTll5Fh/E7LLyU1T20bqmtfpwAPR8I6udDZx5UIHxc6+7rSxdeVCF9X3BwtiU1ogpSQk6DGC5K3QtImNYAM4OKjHoDoyeohcPFuuD5V5Sw9tpRvD33LodxDBLkGMbvvbKZ1nYa9jdErKT0dLr9cDTDPqLvmkkbTRMyfD7NmwYoVam1wIxVVFSw4uoCP9n5EZmkmvX17c33M9UzpPAV720bCYxRlqYbS0ZWq0VSWp/b7dlPeTeFDIWwwdIo8Z5NoQVklSdmqx5+UXcLxnGKScopJPlVKVmF5rbz2toIADyeCPZ0J9nIi0NOZQA9HAj2dCPBQHz93xxYd19CKoQGklJRUVJFbXEFOcQW5xeVkF1WQU1RBTlE52UVqO7OwjKzCck6VnB0z3sHWhgBPR+Of7kyQpxOhnVwI6eSsWgxezuffzZRSjQuk74e03XDyL2UmKs1V6U6eED5MRTiNGAUBvRrtMkspOXzqML8m/Mpvx34jtyyXKK8oboy5kWldp6mwFjXnFkKZjy6+GO6/X01Q0miaAynh99+VMwPA5s3Quze4K7NnmaGMRfGL+CbuG5IKkvBz9mNa12lM6zKNqE71jyecproK0vaonnXiBtWwKi9QaS6+EDIAgvtDUD8I7AWeYec9flZWWUXKqRJSTpWe/qTll5KWV0ZqfikZBWWnxw1N8XZ1wN/dET93R3zdHPF1c8DHzREfVwd83RzxdnXA29UBHzcHnO1tL2i8QysGM0gpGfX6H2QWllNhqDabx9neFl939YfU/Fl+bk4Eejri7+6Ev4cjQZ7OdHKxv/ABqepq5YKXfRSyj0DWIcg8pGYf19y8whb8Y9TNG3KRau34dm9UEdTU98ipI/yR/Acrj6/k6Kmj2NnYMSZ0DLN6zGJw4ODadZg/Xy3TuHEjODjoQWZNy1JSAmFhqufw3Xe1kqplNZtTNzP/0Hw2ntxIlawixjuGyRGTGRc2ji6eXSx7HqurIDNO9bpP/qU+2YeV6QlUo8u/J/j3UK6xft3BJwrcgy165ho8dbUkt6SC9PwyMgvLyCgoJ6NANT6zCsvJLKxplJZTVmn+/eRoZ0OEjysrHjK7llmjaMVQD88vPoCjvQ3eLg50cjmjiX1cHfFxc8D1XE08DSGlGiDLT4H8ZMhLhlNJxk8i5B5TXhU1OHdSN2NAT9ULCOytBtMcLJ+ck1Oaw/aM7WxL28bm1M2cLDqJQNDXry+XdbmMKRFT8HLyOlMgKQm8vVXAsxUrlGL44gsItNweq9E0GX/+qe7FmBhlzpw3Dx58EPz9T2fJKc1hedJylhxbwr7sfQCEu4czPHg4g4MGMyhgUO17vDHKiyDjAGTsU730zIOqkVZmsj61vQt4d1Fzf2o+XuHgGap6GU4eTVF7QDXoiiuqyCkqJ6dYWTJyi5Xl4lRxBQh48uKY8zq2VgzNSXU1lJ6CkmwoylQzM4uyoDANijLUd0Gq+lQU1S5r72K8qTqDT1fwjVbudn49wNX3nFropYZSEvISOJhzkD1Ze9iXvY/EfLVymqu9K4MCBzEubByjQ0fX9g2v6QkkJ0NEBMydCw89dOHXRaNpSr79Vi3+c/CgWjv85ElwdlYNGSMZxRmsS1nH2uS17MjYQamhFIGgi2cX+vj1obdfb3r69KSrV1ccbR0tP7eU6tnOOqTG8rLj1XdNw85Q25kEB3fwDAH3IOMnUH1c/cDNXw2Eu/qCk9cF9zwuBK0YGqOqEsoL1Yu7rED9Li9QrYSyfDVLuCxPKYDSU1CSq2z8Nd/STFfPxl7dDG4B4BGsQk14BINXGHiGq29Xv3N6+VfLanJKczhZdJLjBcdJKkgiKT+J+Lx4ThSeoNooh7eTN318+9DXvy+DAwcT6xOLnY2x92PqXTRlCvTsqXoGAP/9rxpkDgs7++QajbXJzDzTW/jb39Tch6wsdT+npICPj1IWqHk4B7IP8Gfan+zJ2sPe7L3kl6tWv62wpbNHZ7p6dSXCI4JIz0jCPcIJcQvBx8nn3MzCUqoGYF4y5J9Q34VpUHBSNQYL01V6teHsssJWOYc4e5/5du4Ezl7q41Tz8VS9EEf3Mx8Hd7MTUs+FFlcMQoipwH9QK7h9LKV8tU66MKZfglrB7VYp5V+WlDXHeSuGN3uol3tVeeN57V2Nf1inMx8XH6X5XXzU4JWb/5kWgXMni23/pYZS8srzTn9yy3LJKc0hpyyHrJIsMkoyyCzJJK0ojYrqMz7VdsKOUPdQunh2obt3d7p16kYP7x6EuIWomzspSbWsRoxQBW64QXXJ16xR2489BsHBepU1Tdtj927Yu/fMjPtx46CsDLZsUds//qhWEBw5EjDGEitM5lDuIQ6fOsyR3CMkFiSSUphClaw6fVhHW0eCXIMIcAnA38UfPxc/fJx88HH2wdvJGy9HL7wcvfB09MTZztnCsYxq1YAsylRKojgLirOVS3lJtrGBeerMd1keVJY0flw7J2W6euD8GsUtqhiEELbAEWASkIJaA3qWlPKgSZ5LgAdQimEI8B8p5RBLyprjfBVDxfInqBI2VDu4UeXgQrWDq/HbhSoHVwwOblTZOWNwcMYgBAZpwFBtoLKqEoNU3xXVFae/y6vKqahS3+WGckqrSikzlFFqKD39Ka4sPv0prCiksKKw1o1pikuVLZ1lJxwDQ/B3DSC61JWueXY4jhpLuHs4oftOYPfXbmV3BWWDXbpUfQBuvVVNHDp5Um1/8IEKYPbYY+d8rTSaVs2yZWoexDTjqnCdO8Po0fDVV2p7yBCYOhVeeEFtv/IKDBxI5fixJBclU7R8MYnecMSrkrTiNAwnkkiyySdZ5mKoqkRIkHXmIdgJO9wd3HF3cMfV3vX0x9nO+fTHyc4JJ1snnOyccLB1wNHWEQdbBxxsHLC3tT/9bW9jj52NnfoIO+xkNXYVZdhWlmBXUYRtZQk25cXYVpRgU1GstiuKsLN1xH7i8+d1yZpSMVjSdxkMxEspjxlPPh+YAZi+3GcAX0qlZbYKIbyEEEFAhAVlm4ybd/3KS/MSmHNzMDt6uBKTVMorH6bw3G0h7Il2oU98Cf/+9CRP3RXKwUhnBhwu5rnPU3lsdiiHOzsz5GART3+Zyj8eCOdYiBMj9xby+Ddp3PdQZ04EOjJ5Vwn//PYkjz43gMJgH8ZvyeaWz/by1rxrqQzqwsiVR5k47y8W/jIHp+Bwen77O91e/IATCTvpFBSJ+1vvI558UnloODvDv/8Nzz0HlZUqounKT2HOHOVGamNz5lMzbvDII3DPPWcqPHt2c1xGjcb6XHxx7e1du1QPooYBAyAyUv2WEl56CR54APtJk+jiEQnXP0yfJ59U+6uq1PP1wgvIZ5+lIC8dT+9gUp55gMN3zqAo+yRTx81m0/2XsXl6HwyZ6fzjts/56Zb+rBwbhHPmKV59ciPvXRfGj4Pc8M0s5qM3knhzZiB/DPAgLKOc994+zuvXB7GxjzuRqWW8899kXr4piD9j3eiWXMbr/5fMc7cEs7O7K7FJpbz8YQrP3R7CnigX+saX8MKnJ3nq7lAyeoSytsUucv1YohhCgGST7RRUr6CxPCEWlgVACHE3cDdAeHi4BWKdzTV9b8a2549c2e8yxvXqQiffDOy3/sxNg6/iqpgoPP2Scf7rB+4ffhPl3bvi6Z+I+77veGbCPRi6RuIRfATvI1/z7qWPYRPZFdfwfbilfMpP176CQ+cu2EZthZwP+PaqN5Rnj+8GyPmclya+ruyhNhshP4Tr+90Gnp4wKRAqPOnsGwUOrjBpEri5nTFJXX89DB16Zlziscfg0UfPbN97r/rU0KvXeV0XjabN411nYuf//d+Z30JAYaFSAKAUxbp1yqxaw0cfwYABCCHwdPGG558ndMIEQjuPBN9iuG0n46dcyfihYyA/H64o585pN3Dn2LGQkwPrHuKlq+7gpTFjqEo9idz+EC9Nv43SoQMwnEjCY+uLPD7pBmZfFItITMJzy3+5b9S13NAnGodjx3HZ8im3D7uKK2IicPZPwmHrfG4YdAUXR4fg7p6ITa/FXNN/OuXRkc1+KS3BElPSNcAUKeWdxu2bgMFSygdM8iwBXpFSbjRurwEeA7o0VtYcrS0khkaj0bR2WtqUlAKYurWEAqkW5nGwoKxGo9FoWhGWON1uB6KFEJFCCAfgOmBxnTyLgZuFYiiQL6VMs7CsRqPRaFoRjfYYpJQGIcT9wAqUy+mnUsoDQojZxvQPgKUoj6R4lLvqbQ2VbZaaaDQajaZJaJ8T3DQajaaD0ZRjDO17rTuNRqPRnDNaMWg0Go2mFloxaDQajaYWWjFoNBqNphatcvBZCJEFHLe2HOeIL5BtbSFaGF3njoGuc9ugs5TSrykO1CoVQ1tECLGjqTwC2gq6zh0DXeeOhzYlaTQajaYWWjFoNBqNphZaMTQdH1pbACug69wx0HXuYOgxBo1Go9HUQvcYNBqNRlMLrRg0Go1GUwutGJoBIcQjQggphPC1tizNjRDiDSHEISHEXiHEQiGEl7Vlag6EEFOFEIeFEPFCiCesLU9zI4QIE0L8IYSIE0IcEEL83doytRRCCFshxC4hxG/WlsVaaMXQxAghwoBJwAlry9JCrAJ6SSn7AEeAJ60sT5MjhLAF3gMuBmKBWUKIWOtK1ewYgIellDHAUOC+DlDnGv4OxFlbCGuiFUPT8zZqWdMOMaovpVwppTQYN7eiVulrbwwG4qWUx6SUFcB8YIaVZWpWpJRpUsq/jL8LUS/KEOtK1fwIIUKBS4GPrS2LNdGKoQkRQkwHTkop91hbFitxO7DM2kI0AyFAssl2Ch3gJVmDECIC6A/8aWVRWoJ3UA27aivLYVUsWfNZY4IQYjUQaCbpaeApYHLLStT8NFRnKeUvxjxPo8wP37SkbC2EMLO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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "'''График снизу показывает, как меняется форма распределения при увеличение количества степеней свободы.\n", - "А также показывает приближение t-распредееления к нормальному по мере увеличения степеней свободы.'''\n", - "from scipy.stats import t, norm\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "\n", - "\n", - "x = np.linspace(-5, 5, 100)\n", - "y1, y2, y3 = t.pdf(x, df=1), t.pdf(x, df=3), t.pdf(x, df=10)\n", - "y4 = norm.pdf(x)\n", - "\n", - "plt.title('графики t-распредления с разными степенями свободы')\n", - "plt.plot(x, y1)\n", - "plt.plot(x, y2)\n", - "plt.plot(x, y3)\n", - "plt.plot(x, y4, 'r:')\n", - "plt.legend(('df=1', 'df=3', 'df=10', 'norm'))\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "График плотности распределения Стьюдента, как и нормального распределения, является симметричным и имеет вид колокола, но с более «тяжёлыми» хвостами." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Подробно про нормальное и t-распредление\n", - "\n", - "В видео лекциях говорилось, что мы используем t-распределение в ситуации небольшого объема выборки. Необходимо более подробно пояснить, зачем это нужно.\n", - "\n", - "Вернемся к предельной центральной теореме, мы уже узнали, что если некий признак в генеральной совокупности распределен **нормально** со средним $\\mu$ и стандартным отклонением $\\sigma$, и мы будем многократно извлекать выборки одинакового размера n, и для каждой выборки рассчитывать, как далеко выборочное среднее $\\bar{X}$ ˉ\n", - " отклонилось от среднего в генеральной совокупности в единицах стандартной ошибки среднего:\n", - " \n", - "\n", - "$$\\large z = \\frac{\\bar{X} - \\mu}{\\frac{\\sigma}{\\sqrt{n}}}$$\n", - "\n", - "то эта величина z будет иметь стандартное нормальное распределение со средним равным нулю и стандартным отклонением равным единице.\n", - "\n", - "Обратите внимание, что для расчета стандартной ошибки мы используем именно стандартное отклонение в генеральной совокупности - $\\sigma$. Ранее мы уже обсуждали, что на практике $\\sigma$ нам практически никогда не известна, и для расчета стандартной ошибки мы используем выборочное стандартное отклонение.\n", - "\n", - "Так вот, строго говоря в таком случае распределение отклонения выборочного среднего и среднего в генеральной совокупности, деленного на стандартную ошибку, теперь будет описываться именно при помощи t - распределения.\n", - "\n", - "$$\\large t = \\frac{\\bar{X} - \\mu}{\\frac{sd}{\\sqrt{n}}}$$\n", - "\n", - "\n", - "таким образом, в случае неизвестной $\\sigma$ мы **всегда будем иметь дело с t-распределением**. На этом этапе вы должны с негодованием спросить меня, почему же мы применяли z-критерий в первом модуле курса, для проверки гипотез, используя выборочное стандартное отклонение?\n", - "\n", - "Мы уже знаем, что при довольно большом объеме выборки (обычно в учебниках приводится правило, n > 30) t-распределение совсем близко подбирается к нормальному распределению:\n", - "\n", - "Поэтому иногда, для простоты расчетов говорится, что если n > 30, то мы будем использовать свойства нормального распределения для наших целей. Строго говоря, это конечно неправильный подход, который часто критикуют. В до компьютерную эпоху этому было некоторое объяснение, чтобы не рассчитывать для каждого n больше 30 соответствующее критическое значение t - распределения, статистики как бы округляли результат и использовали нормальное распределение для этих целей. Сегодня, конечно, с этим больше никаких проблем нет, и все статистические программы, разумеется, без труда рассчитают все необходимые показатели для t - распределения с любым числом степеней свободы. Действительно при выборках очень большого объема t - распределение практически не будет отличаться от нормального, однако, хоть и очень малые но различия все равно будут.\n", - "\n", - "Поэтому, правильнее будет сказать, что мы используем t - распределение не потому что у нас маленькие выборки, а потому что мы не знаем стандартное отклонение в генеральной совокупности. Поэтому в дальнейшем мы всегда будем использовать t - распределение для проверки гипотез, если нам неизвестно стандартное отклонение в генеральной совокупности, необходимое для расчета стандартной ошибки, даже если объем выборки больше 30.\n", - "\n", - "### 5.Примеры" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "p = 0.065\n" - ] - } - ], - "source": [ - "'''На выборке в 15 наблюдений при помощи одновыборочного t-теста\n", - "проверяется нулевая гипотеза: μ=10 \n", - "и рассчитанное t-значение равняется -2 (t = -2), то p-уровень значимости (двусторонний) равен:\n", - "'''\n", - "from scipy import stats\n", - "\n", - "t = -2\n", - "n = 15\n", - "df = n - 1\n", - "\n", - "p = 2 * stats.t.sf(abs(t), df)\n", - "print(f'p = {p:.3f}')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Сравнение двух средних. t-критерий Стьюдента\n", - "\n", - "t-критерий Стьюдента — общее название для статистических тестов, в которых статистика критерия имеет распределение Стьюдента. Наиболее часто t-критерии применяются для проверки равенства средних значений в двух выборках. Нулевая гипотеза предполагает, что средние равны (отрицание этого предположения называют гипотезой сдвига). Для применения данного критерия необходимо, чтобы исходные данные имели нормальное распределение. \n", - "\n", - "$$ t = \\frac{\\bar{X_1} - \\bar{X_2}}{se}$$\n", - "\n", - "$$ se = \\sqrt{\\frac{sd_1^2}{n_1} + \\frac{sd_2^2}{n_2}} $$\n", - "\n", - "Откуда берётся такая формула $se$?:\n", - "\n", - "$$ (se_1)^2 = (\\frac{sd_1}{\\sqrt{n_1}})^2 = \\frac{sd_1^2}{n_1} $$\n", - " \n", - "То есть:\n", - "\n", - "$$ se = \\sqrt{\\frac{sd_1^2}{n_1} + \\frac{sd_2^2}{n_2}} = \\sqrt{se_1^2 + se_2^2} $$\n", - "\n", - "причем ответ на вопрос, почему верно это равенство, кроется в свойстве дисперсии: дисперсия суммы независимых случайных величин равна сумме их дисперсий. а отклонение - это корень из дисперсии. отсюда ваша последняя формула" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Примеры применения t-критерий Стьюдента\n", - "**Пример 1.** Первая выборка — это пациенты, которых лечили препаратом А. Вторая выборка — пациенты, которых лечили препаратом Б. Значения в выборках — это некоторая характеристика эффективности лечения (уровень метаболита в крови, температура через три дня после начала лечения, срок выздоровления, число койко-дней, и т.д.) Требуется выяснить, имеется ли значимое различие эффективности препаратов А и Б, или различия являются чисто случайными и объясняются «естественной» дисперсией выбранной характеристики.\n", - "\n", - "**Пример 2.** Первая выборка — это значения некоторой характеристики состояния пациентов, записанные до лечения. Вторая выборка — это значения той же характеристики состояния тех же пациентов, записанные после лечения. Объёмы обеих выборок обязаны совпадать; более того, порядок элементов (в данном случае пациентов) в выборках также обязан совпадать. Такие выборки называются связными. Требуется выяснить, имеется ли значимое отличие в состоянии пациентов до и после лечения, или различия чисто случайны.\n", - "\n", - "**Пример 3.** Первая выборка — это поля, обработанные агротехническим методом А. Вторая выборка — поля, обработанные агротехническим методом Б. Значения в выборках — это урожайность. Требуется выяснить, является ли один из методов эффективнее другого, или различия урожайности обусловлены случайными факторами.\n", - "\n", - "**Пример 4.** Первая выборка — это дни, когда в супермаркете проходила промо-акция типа А (красные ценники со скидкой). Вторая выборка — дни промо-акции типа Б (каждая пятая пачка бесплатно). Значения в выборках — это показатель эффективности промо-акции (объём продаж, либо выручка в рублях). Требуется выяснить, какой из типов промо-акции более эффективен.\n", - "\n", - "### 6. Примеры" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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MxSDNSEinterval
Выборка1100.81510.24650320.02.2911884.545754
Выборка275.73515.45810220.03.4565376.886174
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" - ], - "text/plain": [ - " Mx SD N SE interval\n", - "Выборка1 100.815 10.246503 20.0 2.291188 4.545754\n", - "Выборка2 75.735 15.458102 20.0 3.456537 6.886174" - ] - }, - "execution_count": 15, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "import pandas as pd\n", - "from scipy.stats import t\n", - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "\n", - "array1 = np.array([84.7, 105.0, 98.9, 97.9, 108.7, 81.3, 99.4, 89.4, 93.0,\n", - " 119.3, 99.2, 99.4, 97.1, 112.4, 99.8, 94.7, 114.0, 95.1, 115.5, 111.5])\n", - "array2 = np.array([57.2, 68.6, 104.4, 95.1, 89.9, 70.8, 83.5, 60.1, 75.7,\n", - " 102.0, 69.0, 79.6, 68.9, 98.6, 76.0, 74.8, 56.0, 55.6, 69.4, 59.5])\n", - "\n", - "# считаем количество элементов, среднее, стандартное отклонение и стандартную ошибку\n", - "df = pd.DataFrame({'Выборка1':array1, 'Выборка2':array2}).agg(['mean','std','count','sem']).transpose()\n", - "df.columns = ['Mx','SD','N','SE']\n", - "\n", - "# рассчитываем 95% интервал отклонения среднего\n", - "p = 0.95\n", - "K = t.ppf((1 + p)/2, df['Mx']-1)\n", - "df['interval'] = K * df['SE']\n", - "\n", - "df" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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UwdAkSZIkSR0MTZIkSZLUwdAkSZIkSR0MTZIkSZLUwdAkSZIkSR0MTZIkSZLUwdAkSZIkSR0MTZIkSZLUwdAkSZIkSR0MTZIkSZLUwdAkSZIkSR0MTZIkSZLUwdAkSZIkSR0MTZIkSZLUwdAkSZIkSR0MTZIkSZLUwdAkSZIkSR0MTZIkSZLUwdAkSZIkSR0MTZIkSZLUwdAkSZIkSR0MTZIkSZLUwdAkSZIkSR0MTZIkSZLUwdAkSZIkSR0MTZIkSZLUwdAkSZIkSR0MTZIkSZLUwdAkSZIkSR0MTZIkSZLUwdAkSZIkSR0MTZIkSZLUYdmoC5AkSXe1633vy+Xr1gGQhF3Gxrjs6qtHXJUkLU2GJkmSFqDL162jel6nDVCSpOFzeJ4kSZIkdTA0SZIkSVIHQ5MkSQvQLmNjBH77s8vY2IgrkqSly+80SZK0AF129dWMj48DMDk5OdJaJGmp80yTJEmSJHUwNEmSJElSh4GFpiTHJrkmyYU9bfsnuSjJ7UmWT5v/jUl+kOR7SZ45qLokSZIkaS4GeabpOOBZ09ouBJ4PnNXbmGQP4EDg4e0yH0iy+QBrkyQtcbMc3NsuyRlJLmkft+2Z5sE9SVqiBhaaquos4PppbRdX1fdmmH1f4BNV9euq+hHwA+Bxg6pNkiRmPrh3BLC6qnYHVrevPbgnSUvcQvlO0/2BK3ter2nbJEkaiJkO7tEcxFvVPl8F7NfT7sE9SVqiFsolxzNDW804Y7ICWAEwNjbmZViHwPdY0hIyVlVrAapqbZId2vb7A1/rmW/Wg3vz2U/dcMMNgPthSRq1hRKa1gAP6Hm9E3DVTDNW1UpgJcDy5ctr6h4WGhzfY0nq/+DefPZT22yzDeB+WJJGbaEMzzsVODDJPZLsBuwOnD3imiRJS8+6JDsCtI/XtO19H9yTJG16BnnJ8ROArwIPSbImyaFJnpdkDfAE4LNJPg9QVRcBJwLfAT4HvKqqbhtUbZIkzeJU4OD2+cHAKT3tHtyTpCVqYMPzquqgWSadPMv8RwFHDaoewa4778LlV14x5+WSmUalzG6XB+zMZVdcPuftSNIwtQf3xoHt2wN6RwJHAycmORS4AtgfmoN7SaYO7t2KB/ckaUlZKN9p0hBcfuUV1OQ3Br6djD924NuQpI3VcXBv71nm9+CeJC1RC+U7TZIkSZK0IBmaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOiwbdQGSNB+SbNByVTXPlUiSpE2NoUnSJqEr/CQxHEmSpA3m8DxJkiRJ6mBokiRJkqQOhiZJkiRJ6mBokiRJkqQOhiZJkiRJ6mBokiRpgZmYmCAJZ555JmeeeSZJSMLExMSoS5OkJclLjkuStMBMTEwYkCRpAfFMkyRJkiR1MDRJkiRJUgdDkyRJkiR1MDRJkiRJUgdDkyRJkiR1MDRJkiRJUgdDkyRJkiR1MDRJkiRJUgdDkyRJkiR1MDRJkiRJUgdDkyRJ0yR5TZILk1yU5PC2bSLJj5Oc3/48Z8RlSpKGZNmoC5AkaSFJ8gjgFcDjgN8An0vy2Xbyu6vqnSMrTpI0EoYmSZLu7GHA16rqlwBJzgSeN9qSJEmjZGiSJOnOLgSOSnJv4GbgOcA5wHXAq5O8pH39V1X10+kLJ1kBrAAYGxtjcnJyWHVLkgbE0CRJUo+qujjJPwJnADcB3wJuBT4IvAWo9vFdwMtmWH4lsBJg+fLlNT4+PpzCJUkD44UgJEmapqqOqapHV9VTgOuBS6pqXVXdVlW3Ax+m+c6TJGkJMDRJkjRNkh3ax52B5wMnJNmxZ5bn0QzjkyQtAQ7PkyTprj7dfqfpFuBVVfXTJMcn2YtmeN5lwCtHWJ8kaYgGFpqSHAvsA1xTVY9o27YDPgnsStPhvGDqS7RJ3ggcCtwGHFZVnx9UbZIkdamqJ8/Q9uJR1CJJGr1BDs87DnjWtLYjgNVVtTuwun1Nkj2AA4GHt8t8IMnmA6xNkiRJkvoysNBUVWfRfHm2177Aqvb5KmC/nvZPVNWvq+pHwA/wC7aSJEmSFoBhXwhirKrWArSPO7Tt9weu7JlvTdsmSZIkSSO1UC4EkRnaasYZvWngouDfRQuNn0lJkrShhh2a1iXZsarWtpduvaZtXwM8oGe+nYCrZlqBNw1cHPy7aKHxMylJkjbUsIfnnQoc3D4/GDilp/3AJPdIshuwO3D2kGuTJEmSpLsY5CXHTwDGge2TrAGOBI4GTkxyKHAFsD9AVV2U5ETgO8CtNPfEuG1QtUmSJElSvwYWmqrqoFkm7T3L/EcBRw2qHkEduTV8cca3f/63I0mSJG0iFsqFIDQEefPPqMlvDH4744+lJga+GUmSJGkohv2dJkmSJElaVAxNkiRJktTB0CRJkiRJHQxNkiRJktTB0CRJkiRJHQxNkiRJktTB0CRJkiRJHQxNkiRJktTB0CRJkiRJHQxNkiRJktTB0CRJkiRJHQxNkiRJktTB0CRJkiRJHQxNkiRJktTB0CRJkiRJHQxNkiRJktTB0CRJkiRJHQxNkiRJktTB0CRJkiRJHQxNkiRJktTB0CRJkiRJHQxNkiRJktTB0CRJkiRJHQxNkiRJktTB0CRJkiRJHQxNkiRJktTB0CRJkiRJHQxNkiRJktRh2agL0PDs8oCdyfhjh7IdSZIkaVNhaFpCLrvi8jkvk4SqGkA1kiRJ0uLg8DxJkiRJ6mBokiRJkqQOhiZJkiRJ6mBokiRJkqQOhiZJkiRJ6mBokiRJkqQOhiZJkiRJ6mBokiRJkqQOhiZJkiRJ6mBokiRJkqQOhiZJkiRJ6mBokiRJkqQOhiZJkiRJ6mBokiRpmiSvSXJhkouSHN62bZfkjCSXtI/bjrhMSdKQzBqakiwbZiGSJM3FoPqpJI8AXgE8DngksE+S3YEjgNVVtTuwun0tSVoCus40nT31JMk/D6EWSZLmYlD91MOAr1XVL6vqVuBM4HnAvsCqdp5VwH7zuE1J0gLWdZQuPc//cNCFSJI0R4Pqpy4Ejkpyb+Bm4DnAOcBYVa0FqKq1SXaYsahkBbACYGxsjMnJyXksTZI0Cl2hqYZWhSRJczeQfqqqLk7yj8AZwE3At4Bb57D8SmAlwPLly2t8fHwQZUqShqgrND00yQU0R/Ie1D6nfV1VtefAq5MkaXYD66eq6hjgGIAk/wCsAdYl2bE9y7QjcM3GlS9JWiy6QtPDhlaFJElzN7B+KskOVXVNkp2B5wNPAHYDDgaObh9PGdT2JUkLy6yhqaouH2YhkiTNxYD7qU+332m6BXhVVf00ydHAiUkOBa4A9h/g9iVJC4iXFZckaZqqevIMbdcBe4+gHEnSiHlzW0mSJEnqYGiSJEmSpA7rHZ7X3gX9bcAewBZT7VX1wAHWJUlSX+ynJEmD1s+Zpo8CH6S5R8XTgH8Djh9kUZIkzYH9lCRpoPoJTVtW1WogVXV5VU0ATx9sWZIk9c1+SpI0UP1cPe9XSTYDLknyauDHwA6DLUuSpL7ZT0mSBqqfM02HA1sBhwGPAV5Mc1M/SZIWgsOxn5IkDdB6zzRV1TcA2qN4h1XVzwdelSRJfbKfkiQN2nrPNCVZnuTbwAXAt5N8K8ljNmajSV6T5MIkFyU5vG3bLskZSS5pH7fdmG1IkpaGQfRTkiT16md43rHA/66qXatqV+BVNFcq2iBJHgG8Angc8Ehgn/ZysUcAq6tqd2B1+1qSpPWZ135KkqTp+glNP6+qL029qKovAxsz9OFhwNeq6pdVdStwJvA8YF9gVTvPKmC/jdiGJGnpmO9+SpKkO+nn6nlnJ/lX4ASggAOAySSPBqiqc+e4zQuBo5LcG7gZeA5wDjBWVWvbda5NMuOVj5KsAFYAjI2NMTk5OcfNa658j7Up8HO8SZvvfkqSpDtJVXXPkHyxY3JV1ZzvhZHkUJrhEzcB36EJTy+tqm165vlpVXV+r2n58uV1zjnnzHXzmoMkrO8zIi10fo4HK8k3q2r5CLc/7/3UfLGfkqSFYWP7qn7ONP1RVd22oRuYSVUdAxwDkOQfgDXAuiQ7tmeZdgSumc9tSpI2WfPeT0mS1Kuf7zT9IMk7kjxsvjY6NfQuyc7A82mGVJzKHffVOBg4Zb62J0napM17PyVJUq9+QtOewPeBY5J8LcmKJFtv5HY/neQ7wH8Cr6qqnwJHA89IcgnwjPa1JEnrM4h+SpKk3+rn5rY/Bz4MfDjJU2jOCr07yUnAW6rqB3PdaFU9eYa264C957ouSdLSNoh+SpKkXv3c3HbzJM9NcjLwXuBdwANpzhKdPuD6JEnqZD8lSRq0fi4EcQnwReAdVfWVnvaT2iN6kiSNkv2UJGmg+glNL2lvFHgXVXXYPNcjSdJc2U9JkgaqnwtBvG/gVUiStOHspyRJA9XPmaZlSbYF0ttYVdcPpiRJkubEfkqSNFD9hKaHAN/kzp1R0XzJVpKkUbOfkiQNVD+h6TtV9aiBVyJJ0oaxn5IkDVQ/32mSJEmSpCWrn9D0hIFXIUnShrOfkiQNVD/D834nyVuBPYAtphqr6ukDq0qSpP7ZT0mSBqqfM00fBy4GdgPeDFwGfGOANUmSNBf2U5KkgeonNN27qo4BbqmqM6vqZcDjB1yXJEn9sp+SJA1UP8Pzbmkf1yb5Y+AqYKfBlSRJ0pzYT0mSBqqf0PTWJL8L/BXwz8DWwGsHWpUkSf2zn5IkDdR6Q1NVndY+vRF42mDLkSRpbuynJEmDtt7vNCV5YJL/TPKTJNckOSWJd1mXJC0I9lOSpEHr50IQ/w6cCNwXuB/wKeCEQRYlSdIc2E9Jkgaqn9CUqjq+qm5tfz4G1KALkySpT/ZTkqSB6udCEF9McgTwCZpO6ADgs0m2A6iq6wdYnyRJ62M/JUkaqH5C0wHt4yuntb+MpnNy3LgkaZTspyRJA9XP1fN2G0YhkiRtCPspSdKg9XP1vK2S/G2Sle3r3ZPsM/jSJElaP/spSdKg9XMhiI8CvwGe2L5eA7x1YBVJkjQ39lOSpIHqJzQ9qKreDtwCUFU3AxloVZIk9c9+SpI0UP2Ept8k2ZL28q1JHgT8eqBVSZLUP/spSdJA9XP1vCOBzwEPSPJx4A+BQwZZlCRJc2A/JUkaqH6unndGknOBx9MMd3hNVf1k4JVJktQH+ylJ0qCtNzQleUr79Oft4x5JqKqzBleWJEn9sZ+SJA1aP8PzTgXO4s5fqq22TZKkUbOfkiQNVD+h6UdV9dyBVyJJ6/GAXR/AmsvXbNCyydwuprbTLjtx5WVXbtC2NHT2U5KkgeonNNXAq5CkPqy5fA3vuf49Q9nW4dsdPpTtaF7YT0mSBqqf0LRDktdNb6yqfxpAPZIkzZX9lCRpoPoJTR8GfmfQhUiStIHspyRJA9XPJcffPIxCJEnaEPZTkqRB6+eS4/89U3tVPX3+y5EkaW4G0U8leS3wcprvS30beClwBPAK4Np2tr+pqtM3dBuSpMWjn+F59wRuB44Fzh1sOZIkzdm89lNJ7g8cBuxRVTcnORE4sJ387qp658ZuQ5K0uGy2vhmq6g+AlwEPBv4BeFRVfXPQhUmS1I8B9VPLgC2TLAO2Aq7ayPVJkhax9Yam1neBL9Lcbf1xgytHkqQNMm/9VFX9GHgncAWwFrixqr7QTn51kguSHJtk243ZjiRp8ejnO03/ADwG+DzwF1V17XoWkSRpaOa7n2rD0L7AbsANwKeSvAj4IPAWmu85vQV4F80ZrunLrwBWAIyNjTE5Obkx5UiSFoB+vtN0BPAL4InARJIAVVVbD7QySZL6M9/91B8BP5oKX0k+Azyxqj42NUOSDwOnzbRwVa0EVgIsX768xsfHN7AMSdJC0c8lx/sdwidJ0tANoJ+6Anh8kq2Am4G9gXOS7FhVa9t5ngdcOM/blSQtUOvtaNJ4UZL/275+QBK/1yRJWhDmu5+qqq8DJ9Fcie/bNH3lSuDtSb6d5ALgacBrN756SdJi0M/wvA/QXMr16TRjuG8C/gV47ADrkiSpX/PeT1XVkcCR05pfvKHrkyQtbv2Epj+oqkcnOQ+gqn6a5O4DrkuSpH7ZT0mSBqqfceC3JNmc5mpBJLkPzRE9SZIWAvspSdJAzRqa2hv6AbwPOBnYIclRwJdpbh4oSdLI2E9Jkoala3je2cCjq+rjSb5Jc/WgAPtV1cVDqU6SpNnZT0mShqIrNGXqSVV9l+Zu65IkLRT2U5KkoegKTfdJ8rrZJlbVPw2gHkmS+mU/JUkaiq7QtDlwL3qO5EmStIDYT0mShqIrNK2tqr8fWiWSJM2N/ZQkaSi6LjnukTtJ0kJmPyVJGoqu0LT30KqQJGnu7KckSUMxa2iqquuHWYgkSXNhPyVJGpauM02SJEmStOR1XQhCS0TS/bWArulVNd/lSJIkSQuKoUkGH0mSJKmDw/MkSZIkqYOhSZIkSZI6GJokSZIkqYOhSZIkSZI6jCQ0JXltkouSXJjkhCRbJNkuyRlJLmkftx1FbZIkSZLUa+ihKcn9gcOA5VX1CGBz4EDgCGB1Ve0OrG5fS5IkSdJIjWp43jJgyyTLgK2Aq4B9gVXt9FXAfqMpTZIkSZLuMPT7NFXVj5O8E7gCuBn4QlV9IclYVa1t51mbZIeZlk+yAlgBMDY2xuTk5JAql7TUuH+RJEkwgtDUfldpX2A34AbgU0le1O/yVbUSWAmwfPnyGh8fH0CVkgTuXyRJEoxmeN4fAT+qqmur6hbgM8ATgXVJdgRoH68ZQW2SJEmSdCejCE1XAI9PslWSAHsDFwOnAge38xwMnDKC2iRJkiSN2MTEBEnu8jMxMTGSekbxnaavJzkJOBe4FTiPZrjdvYATkxxKE6z2H3ZtkiRJkkZvYmKCiYmJ3w6VH/X3jIcemgCq6kjgyGnNv6Y56yRJkiRJC8aoLjkuSZIkSYuCoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSJEmSOhiaJEmSJKmDoUmSpGmSvDbJRUkuTHJCki2SbJfkjCSXtI/bjrpOSdJwGJokSeqR5P7AYcDyqnoEsDlwIHAEsLqqdgdWt68lSUuAoUmSpLtaBmyZZBmwFXAVsC+wqp2+CthvNKVJkobN0CRJUo+q+jHwTuAKYC1wY1V9ARirqrXtPGuBHUZXpSRpmJaNugBJkhaS9rtK+wK7ATcAn0ryojksvwJYATA2Nsbk5OQAqpSkpeGGG24AGPm+1NAkSdKd/RHwo6q6FiDJZ4AnAuuS7FhVa5PsCFwz08JVtRJYCbB8+fIaHx8fTtWStAnaZpttABj1vtTheZIk3dkVwOOTbJUkwN7AxcCpwMHtPAcDp4yoPknSkHmmSZKkHlX19SQnAecCtwLn0Zw5uhdwYpJDaYLV/qOrUpI0TIYmSZKmqaojgSOnNf+a5qyTJGmJcXieJEmSJHUwNEmSJElSB0OTJEmSJHUwNEmSJElSB0OTJEmSJHUwNEmSJElSB0OTJEmSJHUwNEmSJElSB0OTJEmSJHUwNEmSJElSh2WjLkCS+lVHbg3v/buhbOs1R249lO1IkqSFz9AkadHIm3/Ge65/z1C2dfh2h1MTQ9mUJEla4ByeJ0mSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdhh6akjwkyfk9Pz9LcniS7ZKckeSS9nHbYdcmSZIkSdMNPTRV1feqaq+q2gt4DPBL4GTgCGB1Ve0OrG5fS5IkSdJIjXp43t7AD6vqcmBfYFXbvgrYb1RFSZIkSdKUZSPe/oHACe3zsapaC1BVa5PsMNMCSVYAKwDGxsaYnJwcRp2SliD3L5IkCUYYmpLcHXgu8Ma5LFdVK4GVAMuXL6/x8fH5L06SAPcvkiQJRjs879nAuVW1rn29LsmOAO3jNSOrTJIkSZJaowxNB3HH0DyAU4GD2+cHA6cMvSJJkiRJmmYkoSnJVsAzgM/0NB8NPCPJJe20o0dRmyRJkiT1Gsl3mqrql8C9p7VdR3M1PUmSJElaMEZ9yXFJkiRJWtAMTZIkSZLUwdAkSZIkSR0MTZIkSZLUwdAkSZIkSR0MTZIkSZLUwdAkSZIkSR0MTZIkSZLUwdAkSZIkSR2WjboASZIkSZpu1/vel8vXrQMgCbuMjXHZ1VePpBZDkyRJkqQF5/J166ie12kD1Cg4PE+SJEmSOhiaJEmSJKmDoUmSJEnSgrPL2BiB3/7sMjY2slr8TpMkSZKkBeeyq69mfHwcgMnJyZHW4pkmSZIkSergmSZJknokeQjwyZ6mBwJ/B2wDvAK4tm3/m6o6fbjVSZJGwdAkSVKPqvoesBdAks2BHwMnAy8F3l1V7xxddZKkUXB4niRJs9sb+GFVXT7qQiRJo+OZJkmLxk677MTh2x0+tG1JwIHACT2vX53kJcA5wF9V1U9HU5YkaZgMTZIWjSsvu3KDlktCVa1/RqlHkrsDzwXe2DZ9EHgLUO3ju4CXzbDcCmAFwNjY2Miv+CRJi9kNN9wAjP7qeYYmSZJm9mzg3KpaBzD1CJDkw8BpMy1UVSuBlQDLly+vqcvlSpLmbptttgFg1PtSv9MkSdLMDqJnaF6SHXumPQ+4cOgVSZJGwjNNkiRNk2Qr4BnAK3ua355kL5rheZdNmyZJ2oQZmiRJmqaqfgnce1rbi0dUjiRpxByeJ0mSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdDE2SJEmS1MHQJEmSJEkdRhKakmyT5KQk301ycZInJNkuyRlJLmkftx1FbZIkSZLUa1Rnmt4LfK6qHgo8ErgYOAJYXVW7A6vb15IkSZI0UkMPTUm2Bp4CHANQVb+pqhuAfYFV7WyrgP2GXZskSZIkTTeKM00PBK4FPprkvCQfSXJPYKyq1gK0jzuMoDZJkiRJupNlI9rmo4G/rKqvJ3kvcxiKl2QFsAJgbGyMycnJgRQpadPivkKSJG2oUYSmNcCaqvp6+/okmtC0LsmOVbU2yY7ANTMtXFUrgZUAy5cvr/Hx8SGULGmxc18hSZI21NCH51XV1cCVSR7SNu0NfAc4FTi4bTsYOGXYtUmSJEnSdKM40wTwl8DHk9wduBR4KU2AOzHJocAVwP4jqk2SJEmSfmskoamqzgeWzzBp7yGXIkmSJEmdRnWfJkmSJElaFAxNkiRJktTB0CRJkiRJHQxNkiRJktTB0CRJkiRJHQxNkiRJktTB0CRJkiRJHQxNkiRJktTB0CRJUo8kD0lyfs/Pz5IcnmS7JGckuaR93HbUtUqShsPQJElSj6r6XlXtVVV7AY8BfgmcDBwBrK6q3YHV7WtJ0hJgaJIkaXZ7Az+sqsuBfYFVbfsqYL9RFSVJGi5DkyRJszsQOKF9PlZVawHaxx1GVpUkaaiWjboASZIWoiR3B54LvHGOy60AVgCMjY0xOTk5/8VJ0hJxww03AIx8X2pokiRpZs8Gzq2qde3rdUl2rKq1SXYErplpoapaCawEWL58eY2Pjw+lWEnaFG2zzTYAjHpf6vA8SZJmdhB3DM0DOBU4uH1+MHDK0CuSJI2EoUmSpGmSbAU8A/hMT/PRwDOSXNJOO3oUtUmShs/heZIkTVNVvwTuPa3tOpqr6UmSlhjPNEmSJElSB0OTJEmSJHUwNEmSJElSB0OTJEmSJHUwNEmSJElSB0OTJEmSJHUwNEmSJElSB0OTJEmSJHUwNEmSJElSB0OTpE1Ckll/uqZLkqSFZ2JigiSceeaZnHnmmb/ttycmJkZSz7KRbFWS5llVjboESZI0TyYmJkYWkGbimSZJkiRJ6mBokiRJkqQOhiZJkiRJ6mBokiRJkqQOhiZJkiRJ6mBokiRJkqQOhiZJkiRJ6mBokiRJkqQOhiZJkiRJ6mBokiRJkqQOhiZJkiRJ6mBokiRJkqQOhiZJkiRJ6mBokiRJkqQOhiZJkiRJ6mBokiRJkqQOhiZJkiRJ6mBokiRJkqQOhiZJkiRJ6mBokiRJkqQOqapR17DBklwLXD7qOjZx2wM/GXUR0kbyczxYu1TVfUZdxEI0T/2Un19JS9187Ac3qq9a1KFJg5fknKpaPuo6pI3h51iLmZ9fSUvdQtgPOjxPkiRJkjoYmiRJkiSpg6FJ67Ny1AVI88DPsRYzP7+SlrqR7wf9TpMkSZIkdfBMkyRJkiR1MDQtYkluS3J+km8lOTfJE+ew7FOSnJ7k7CSnDbLOadt9dZIfJKkk2w9ru1q4Funn+ONJvpfkwiTHJrnbsLathWWRfn7dD0uaV4t0XzinvtzheYtYkpuq6l7t82cCf1NVT+1juT2ADwGHVNWlAy5z+rYfBfwUmASWV5X3HlniFunn+DnAf7Uv/x04q6o+OMwatDAs0s+v+2FJ82qR7gvn1Jd7pmnTsTVNJ0iS8elJPcn2SS5rXx4CFHBakm8nOaCdJ0ne0Sbu3vbxJGclOTnJd5J8KMlm7bSb2sf7tkcYHtm+/mCSc5JclOTNU3VU1XlVNVWHNN1i+RyfXi3gbGCnwb0lWkQWy+fX/bCkQVos+8I59eXLNvZd0UhtmeR8YAtgR+DpfS53H+A3wO/T3GH5G0nOAp4I7AU8clo7wOOAPWjubP854PnASQBJtgb+A3htVX2rnf9NVXV9ks2B1Un2rKoLNvxX1SZs0X6O05zKfzHwmrn/2tpELNrPryTNo0W7L+y3L/dM0+J2c1XtVVUPBZ4F/FuStNOe3Kbs85K8bNpyAU6oqtuqah1wJvBY4EmztAOcXVWXVtVtwAntvNB8hk4G1lXVF3u28YIk5wLnAQ+n+XBLM1nMn+MP0JzO/9JGvgdavBbz51eS5sti3hf21ZcbmjYRVfVVmiR+n7bpS1W1F/AM4O3AVj2z/2yW1WSWdmhOnc70ekvgP4GtkzwdIMluwOuBvatqT+CzNEcepE6L6XOc5Mi2ztd1/1ZaKhbT51eSBmUx7Qvn0pcbmjYRSR4KbA5cN23Sz4Fb22lTvg4ckGTzJPcBnkIzlvOsWdoBHpdkt3bc6AHAl9v2X1TVe4BXAu9LsiXNWNZfADcmGQOePb+/rTZVi+VznOTlwDOBg6rq9vn57bXYLZbPryQN0mLZF861L/c7TYvb1PhRaBL5wVV1W3s29IlJvgzcE3g3zQd1yidoxopeANwGvKGqrk5yMvAE4Fs0qX2q/aHAV4GjacacnkVz+vO3qur7Sf4deHNVvSHJecBFwKXA/0zNl+Qw4A3AfYELkpxeVS+ft3dEi9Gi+xzTXOnncuCrbZ2fqaq/n5d3Q4vNovv8uh+WNACLbl/IHPtyLzmu9UoyDry+qvYZcSnSBvNzrMXMz68kjXZf6PA8SZIkSergmSZJkiRJ6uCZJkmSJEnqYGiSJEmSpA6GJkmSJEnqYGjSSCW5b5JPJPlhku8kOT3Jg0dd11LW3hPhDUm+kuTcJK8YdU2SNCr2UwuP/ZRGwfs0aWTSXBT/ZGBVVR3Ytu0FjAHfH2FpS90EcDvN3bNvHnEtkjQy9lML1gT2UxoyzzRplJ4G3FJVH5pqqKrzq+pLScaTnJXk5PbI3ofaOz+T5INJzklyUZI3Ty2b5LIk307y3SRfSHLPtv2mnnmWJ5lsn98zybFJvpHkvCT7tu2HJHl/zzLvT3JIzza2b59/LMmF7fPNk7yjXdcFSV450y+cZPskv0lyfpIfJDmtbR9PcmPbfmmS17XtX2o76Knl/yfJnknel+Tv2rZntu/VZtO2NZHkx209303y9Lb9uCR/Om3e1yeZaF++EHgycHaS1Ul2bufZpX19wbT249q/z5eSfD/JPm37Fkk+2v5NzkvytOnvb5IDk3w+yd1mer8kacTsp+yn7KcEGJo0Wo8Avtkx/XHAX9Hc8flBwPPb9jdV1XJgT+CpSfbsWeZpwMNpjgI+aD3bfxPw31X12Ha5d0x1YOuT5Pfb+qccCtzYruuxwCuS7DbDopsDa6pqL+Dl06Z9qW0/AHhR2/YR4JB2mw8G7lFVFwBHAAe0O/j3AS+tqttn2N67q2pP4Big3xvB7UZzVPX3gY+36wd4P/Bv7fp62wF2BZ4K/DHwoSRbAK8CaNdzELCqbaf9ffYGXgP8aVXd0mdtkjRM9lN3Zj+lJcvQpIXs7Kq6tKpuA04AntS2vyDJucB5NB3PHj3LfBG4ElgHfLtt27I9MnY+zU50yv8CjmjbJ4EtgJ3baQf0LHPADLW9FThy2rpe0s7/deDewO4zLHcv4PpZft8nt8t/kTt29J8C9mmPcL0MOA6gqn4JvAI4A3h/Vf1wlnW+Nsl3gL8GPtrT/o7291udu47Nvx349/b58dzxvj9hlnaAE6vq9qq6BLgUeGg7/fi23u8ClwNT2/p9miEvb6+qn89SuyQtdPZT9lNaIgxNGqWLgMd0TJ9+5+Vqj4q9nmYc857AZ2k6kSlPA+5P0xkd1LbdXFV7tUfHXtgzb4D/b2paVe1cVRe30z7Zs8wnp9XxROAm4FvT1vWXPevaraq+MMPvtBuwZpbfd+oI3q7Am5Ns0XY6ZwD7Ai/gjs4Amh36dcD9ZlkfNEfw9gAOBN7V0/5/2m2dQDM2vNf0zmG2O2BXxzxF857M5mHAn9H+nh3zSdIo2U/dmf2UlixDk0bpv4F7pOeqN0kem+Sp7cvHJdmtHQN9APBlYGvgF8CNScaAZ09faVUVzQ51+/Vs//PAXyZJu+1H9Vn3BPB3M6zrL6bGPCd58CxDKPYHTlvP+n8JbAnco339EZojet+oquvb9e9CMyTkUcCzk/zBetb5M2Z+P64D7j6t7Rs0nRc0nfeX2+dfmaUdYP8kmyV5EPBA4HvAWe18U0M2dm7boTnidxpwEnd9LyVpobCfmpn9lJYcr56nkamqSvI84D1JjgB+BVwGHE5zFO6rwNE0R6rOAk6uqtuTnEdz9O9S4H+mrfaLSYrmCN7frKeEtwDvAS5oO6TL6G889der6odJdu1p+wjNkbdz23VdC+zXu1CS/w2soBnf/mqaIRD3SfJcms5iatjDFsA/VdWNAFX1zSQ/ox220K7/GOD1VXVVkkOB45I8tqp+Na3W1yZ5Ec2/9df3/u5JDqfp8F4JPL1n2quBY5L8H+AamuEWAIcBx7bt1wIv7Vnme8CZNGP0/7yqfpXkAzTjxr8N3AocUlW/bvv+KW+j+SLvJ9ox8JK0YNhP2U9hP6VWmoMd0sKSZJxmZ9vvl0IXvDRX/Zmsqsmetn2A7avquI7l7kczlv2hs3yJdqSSHAecVlUnjboWSRoW+6k7LWc/pU2eZ5qk4TmJ5ohYr3O5Y3jDXSR5CXAU8LqF2BFJkjYp9lPSLDzTJEmSJEkdvBCEJEmSJHUwNEmSJElSB0OTJEmSJHUwNEmSJElSB0OTJEmSJHUwNEmSJElSh/8H0sMdX8jBK/YAAAAASUVORK5CYII=\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "\n", - "\n", - "#строим графики, boxplot из изначальных данных array1, array2, доверительные интервалы из датафрейма df\n", - "fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(14, 9))\n", - "\n", - "# график boxplot\n", - "bplot1 = ax1.boxplot([array1, array2],\n", - " vert=True, # создаем вертикальные боксы\n", - " patch_artist=True, # для красоты заполним цветом боксы квантилей\n", - " labels=['Выборка1', 'Выборка2']) # используется для задания значений выборок в случае с boxplot\n", - "\n", - "# график доверительных интервалов\n", - "bplot2 = ax2.errorbar(x=df.index, y=df['Mx'], yerr=df['interval'],\\\n", - " color=\"black\", capsize=3, marker=\"s\", markersize=4, mfc=\"red\", mec=\"black\", fmt ='o')\n", - "\n", - "# раскрасим boxplot \n", - "colors = ['pink', 'lightgreen']\n", - "for patch, color in zip(bplot1['boxes'], colors):\n", - " patch.set_facecolor(color)\n", - " \n", - "# добавим общие для каждого из графиков данные\n", - "for ax in [ax1, ax2]:\n", - " ax.yaxis.grid(True)\n", - " ax.set_title('Температура плавления ДНК двух типов')\n", - " ax.set_xlabel('Сравнение двух выборок')\n", - " ax.set_ylabel('Температура F')\n", - " \n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Задача \n", - "\n", - "Рассчитайте доверительный интервал основываясь на знании t - распределения для среднего значения температуры плавления ДНК у первого вида:\n", - "\n", - "$$ \\bar{X}=89,9\\quad sd=11,3\\quad n=20 $$" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[84.61; 95.19]\n" - ] - } - ], - "source": [ - "from scipy import stats\n", - "from math import sqrt\n", - "\n", - "mean = 89.9\n", - "sd = 11.3\n", - "n = 20\n", - "# степень свободы\n", - "df = n - 1\n", - "# 95% доверительный интервал\n", - "p = 0.95\n", - "alpha = 1-p\n", - "# стандартная ошибка\n", - "se = sd/sqrt(n)\n", - "\n", - "# ppf - Percent point function\n", - "# делим на два, так как по умолчанию функция считает для одного конца, а нам надо для двух\n", - "t_value = stats.t(df).ppf(1-(alpha/2))\n", - "\n", - "# доверительный интервал \n", - "сonfidence_interval = (mean-t_value*se, mean+t_value*se)\n", - "print('[%.2f; %.2f]' % сonfidence_interval)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Первые премии Оскар за лучшую мужскую и женскую роль были вручены в 1929. Данные гистограммы демонстрируют распределение возраста победителей с 1929 по 2014 год (100 мужчин, 100 женщин). Используя t - критерий проверьте, можно ли считать наблюдаемые различия в возрасте между лучшими актрисами и актерами статистически достоверными.\n", - "\n", - "Средний возраст мужчин равен 45, sd = 9.\n", - "\n", - "Средний возраст женщин равен 34, sd = 10.\n", - "\n", - "" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "p=5.328933875539173e-13\n", - "Мы можем отклонить нулевую гипотезу\n" - ] - } - ], - "source": [ - "from scipy.stats import t\n", - "from numpy import sqrt\n", - "\n", - "mean_m, mean_f = 45, 34\n", - "sd_m, sd_f = 9, 10\n", - "N = 100\n", - "\n", - "se = sqrt((sd_m ** 2)/N + (sd_f ** 2)/N)\n", - "t_value = (mean_m - mean_f)/se\n", - "\n", - "p = t.sf(t_value, N-2)\n", - "print(f'p={p}')\n", - "if p >= 0.05:\n", - " print('Мы НЕ можем отклонить нулевую гипотезу')\n", - "else:\n", - " print('Мы можем отклонить нулевую гипотезу')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Проверка распределения на нормальность\n", - "\n", - "### QQ-plot\n", - "\n", - "Эту тему пока сам не понял, так что инфы мало((\n", - "\n", - "### 7.Примеры\n" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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XUK6cL7lCaBbQwsyaAWuBXsB1YThX5IhabFpJz8UT6bloIo22b2BfqTKkHnc637Q8h19rNmLCkL9Bnz4wcSKUUskikUl/M0UkrjRu7LV2ACQzjs+5ih9pR/9GI1hQoYK/4ULAOXfQzO4CxgCJwLvOuYVmdkfg+TfM7BhgNlAFyDSz+4CWzrkdeZ3ryyciMaP+jo1cumgSPRdN4KRNKzhoCUxtegovnHUdY1ucwa6yQf8OBw70diB95hl47DH/QosUQMW0iMSsvC40fPppr0f61D2T+Yae/MyJXFF+NM/9q4rfcUPGOTcKGHXYsTeC7v+O18JRqHNFiiUjA666imlffQXAD/VP4LHk2xl14llsrlg973OuvRZGjoR//hPOPx86dQpjYJHCUTEtIjEpvwsNBw2CLx6axVlPXMwq15hbG47luWdreKt5iEjofPEFfPUVb7fvyQenXcLqascU7rzXXoMpU7x2jx9/hMqVQ5tTpIhUTItITMrrQsM9e+CjB39i9L4LoGktTpyUyuyGdf0JKBJPMjPhqaegZUue7norzoqw7GTVqjB4MJxzDtx7L7z7buhyihRDTCyiKiJyuMMvNAQ4niV8sL4bVKgAaWnQMM/OBhEpaV9/DQsWwIABRSuks5x1FjzyCLz3njfDLRJBVEyLSEw6fN+QpvxGGkkkJjhITdVSWyLh4pw3K92iBVxzTfFf5/HHoUMHr19rzZqSyydylFRMi0hMevppbwIaoAFrSCOJCuxhxlOpcOKJ/oYTiScjR3q9zo8+enSbIZUu7V0MkZ4ON93ktY6IRAAV0yISk3r39i42PLXhRlJJprZtZsY/xnDxI238jiYSP5yDJ5+Epk0pkat8W7SAF1/02rReeOHoX0+kBKiYFpGY1bv7VubU6MaJ5VdReeJIuj/Wwe9IIvFl3DiYOdPrdy6pnUVvvRUuv9x7zblzS+Y1RY6CimkRiU07dkD37vDzz97FT126+J1IJL5kzUo3bAg33lhyr2sGb70FtWp5G7ocvmyPSJipmBaR2LNnD/ToAXPmwJAh3mYPIhJeEyd660M/9BCULVuyr12zJnzwASxeDH/7W8m+tkgRqZgWkdiyf7/3K+ApU7y1aXv29DuRSHx68kk45hivLSMUunWD++/3NnUZpU06xT8qpkUkdhw44C29NXYsvP029OrldyKR+DRtGowfDw8+COXLh+59nnkGWreGm2+GjRtD9z4iBVAxLSIx4eOPMhhW7Qb45hseq/4KKWVv8TuSSPx68kmvp/n220P7PuXKwccfw/bt8PDDoX0vkXyomBaRqJfyUSYHbu7LpXs+5SGe5ck/7qJvX29JWhEJs1mzYPRoeOABqFgx9O938snQpw98/jns3Rv69xM5jIppEYlaKSnQtIljyw33cWPGuzzJ//FvHgK8axAHDPA5oEg8euopqF4d7rwzfO957bWwa5d6p8UXKqZFJCqlpEDfPztuX/Uo9/AK/+N+HuOfOcasWuVTOJF4NW8eDBsG990HlSuH733PPRfq1oVPPw3fe4oEqJgWkag0YADct/cZHuFZ3uB2HuC/gOUY07ixP9lE4tZTT0GVKnDPPeF938REuOoqGDECdu4M73tL3FMxLSJR6fKVL/I0/8dH9KE/r3N4IV2hAjz9tD/ZROLSokUwdCjcfTdUqxb+9+/VC/bt82bGRcJIxbSIRJWUFHik5iBe4H6GcgU38x7usG9lTZrAoEHQu7dPIUXi0dNPez/F3nefP+9/xhnQqBF88ok/7y9xS8W0iES8lBRo2tTbRXh0n8E8vfUORtGda/mEDEodGlehgrdPy4oVKqRFwuqXX7x+5f79vSXx/JCQ4M1OjxkDW7f6k0HikoppEYk4wcVzQoK36tXKlXA5X/IeNzGRc/gTQzlAmUPnaDZaxEfPPONtGf7AA/7m6NULDh6EL7/0N4fElVJHHlI8ZtYI+BA4BsgEBjnnXjKzGsBnQFNgBXC1c+6PUOUQkeiSkgJ9+3pL2wE4591eyLd8Si9m0YFLGcY+sndVM/Nmo0Uk/Bpt+937ldDdd3sravik6cMjwTnGV6/Puqdepc/SevmOXfHsxWFMJrEulDPTB4EHnHMnAZ2AO82sJfAwkOacawGkBR6LSJxLSfF+O9ynT3YhneUcJvAlV7CAk+nOt+wi55JbWrVDxD/9pn8OpUp5W4f7zYzhJ53NGavmU3uX5ukkPEJWTDvn1jvnfgjc3wksBhoAPYEPAsM+AC4LVQYRiXzBRfSWLbmf78T3jKAHyzmW8xnLdqrleF6rdoj4p+renVw5Pw1uuQXq1/c7DgDDTzqbRJdJ9yVT/I4icSIsPdNm1hRoB8wA6jrn1oNXcAN1wpFBRCJLSgpUqpR/EQ1wCj/yLd35nWNIJpUteBc2WWAVPPVJi/jrnN/mUCbzINx0k99RDllaqzGLazfl0sWT/I4icSLkxbSZVQKGAvc553YU4by+ZjbbzGZv2rQpdAFFJOxSUuDmm2H37vzHnMQixnI+O6hCEmn8jtf/WLMmfPSR10utVTtE/JW8dCabKlSD9u39jpLD8JPOpv3axTTYvtHvKBIHQlpMm1lpvEI6xTmXdWntBjOrF3i+HpDn33Tn3CDnXHvnXPvatWuHMqaIhNmAAXDgQP7PN2cpqSRzkFIkkcYqmtCkiXeN0+bNKqBFIkGpjIOcs3wO3zVv7y27E0GGn3Q2ABf/PNnnJBIPQva338wMeAdY7Jz7X9BTw4AbA/dvBL4JVQYRiTwpKd4yd/lpxCrSSKIM6XQvlcoTg1toFlokAp22djFV9+8m7biOfkfJZXW1Y5hb73guUauHhEEof5TsDFwPdDWzuYGPi4BngW5m9ivQLfBYROJA1rJ3+TmG9aSRRDW2cXXVsTz4fisV0CIRKmnpTPYnlmJKk1P8jpKn4SedTesNy2i2da3fUSTGhXI1jynOOXPOtXHOnRL4GOWc2+KcS3LOtQjcapsikTgxYEDuZe+y1GQz4+hGo1LrqTr1W8ZvO1WFtEgES1o2ixmNWrO7bAW/o+RpxIlnkYnRQ7PTEmKR1eQkIjFt1aq8j1dhO2mJF3BS6aWUGzMMzjwzvMFEpEiabl1L861rIrLFI8uGyrWY1aiVt6pH1u5PIiGgYlpEwiIlJXtJu2AV2UVa2YtomzCfxK+GQteu4Q8nIkWStGwWAGnNO/icpGDDTjqbFltWc+KmFX5HkRimYlpEQi5rKbzMzJzHy7GX4daTU9Onw8cfw8Xa4lckGnRdNpMltRqzptoxfkcp0LcndOagJehCRAkpFdMiEnL33pt7KbzSpPM5V3GeG0/CB+/DlVf6kk1Eiqby/t10XL2Q8c0jt8Ujy9YKVZna9BSvmFarh4SIimkRCan+/XPvcJjIQVLoTQ9G0o+BcP31/oQTkSLr8tuPlM7MIDWC+6WDDT/pbBpv30Db9b/4HUVilIppEQmJrO3CBw7MedzI5B1u5Sq+4C/8l2+b3OFPQBEplqSlM/ijXGV+rH+C31EKZWyLTuxPLKVWDwkZFdMiUuL694c+ffLaLtzxGndyIx/yGP/gtTJ/4emn/UgoIsWRkJnBeYFdDzMTEv2OUyg7ylViwrHt6fHzZBIyM/yOIzFIxbSIlKiUlNyz0R7Hf3iQfrzBc/yNp+3vvPuudjUUiSanrPuFGnt3kBYF/dLBhp90Nsfs2kqHNYv8jiIxSMW0iJSoe+/N+/jj/IO/8l9e5U4e4Vk+/MhUSItEmeRlMziQkMjkZu38jlIkac07sqd0WbV6SEiomBaREpPXxYYAf+U/PME/eI+buIeXuaOfCmmRaNR16SxmNWzFjnKV/I5SJHvLlCP1uNPpvmQqpTIO+h1HYoyKaREpEcnJebd39ON1/sPf+JRruI23uaNfAq+/Hv58InJ0Gm7fwImbV0b8Ri35GX7S2dTcu4MzV87zO4rEGBXTInLU+veHtLTcx2/kfV7nToZxCdfzEbf3S1QhLRKlui6dCRDRW4gXZGKz09hRtiKXLJ7sdxSJMaX8DiAi0S2/Cw6vYgjvcCtj6UYvG8L7H5VWa4dIFEtaNotlNRqwokYDv6MUS3qp0ow+/gwuXDIN9u2DcuX8jiQxQjPTIlIsWetI9+mT+7keDCeF3kzjTK7gK976qJwKaZEoViF9L51W/cT4KG3xyDL8pLOpkr4HRo/2O4rEEM1Mi0iRJSfn3dYBkEQqX3AlczmFixnJDf0qqpAWiXJdVvxI2YyDYW/xaPrwyBJ9vWlN2rKlfBVqfvYZXHZZib62xC/NTItIkeTXHw3QmSl8Q0+WcAIXMIaOSVXUIy0SA7ouncWOshWZ3aCl31GOSkZCIhOat4fUVMjM9DuOxAgV0yJSJG++mffx05jNKC5iDQ3pxjjSK9YgNTW82USk5JnLpOvyWUxsdioHE6P/F9pTm7SFzZthwQK/o0iMUDEtIoXWv3/ekzknM58xXMAWapJEGhupm2/RLSLRpc36X6m9e1vUruJxuO8bt/HujB/vbxCJGSqmRaRQ8lu1owW/MI5u7KMcSaSxlob066dtwkViRddls8iwBCYce5rfUUrE+iq1oUWL/PvVRIpIxbSIFModd+Q+1oQVpJFEApkkkcamSscyeDDqkxaJIUnLZjGnwYlsK1/F7yglp2tXmDgRDmo3RDl6KqZF5Ij694ddu3Ieq89a0kiiErvoxjj+PvhEdu7UjLRILDlmx2ZO3rCM8c1jo8XjkK5dYedOmDPH7yQSA1RMi0iB+vfP3d5Rm42kkkwdNnIho1lbs62KaJEY1HX5LABSY6Rf+pDzzvNu1TctJUDFtIjkK68+6Wr8wVjOpwkruZiRzOR0XnrJn3xSOGZ2oZktMbOlZvZwHs+bmb0ceP4nMzs16Ln7zWyhmS0ws0/MTNvGxZGuS2eyqmpdltZs5HeUklW7NrRpo2JaSoSKaRHJ17335nxciZ18S3dOYjGX8xWTOVsXG0Y4M0sEXgO6Ay2Ba83s8MWCuwMtAh99gYGBcxsA9wDtnXMnA4lArzBFF5+VO7CPs1bO81bxMPM7Tsnr2hWmTPG2Fhc5CiqmRSRP/fvDli3Zj8uzhxH0oD2zuZohjOUCKlbUxYZRoCOw1Dm33DmXDnwK9DxsTE/gQ+eZDlQzs3qB50oB5c2sFFABWBeu4OKvM1f+RLmD6aTFWr90lq5dvUJ6+nS/k0iUi/7V10WkxB3e3lGG/XzJFXRhMr1JYVigFtNa0lGhAbA66PEa4PRCjGngnJttZs8Dq4C9wFjn3Ni83sTM+uLNatO4ceMSii5+Slo2k11lyjOz0clHHFvS236HWtOHR1J5/17mWgKvDniTF7rsznfsimcvDmMyiUaamRaRXILbO0pxgE/pxYWM4c+8xadcC6D2juiR1+/nXWHGmFl1vFnrZkB9oKKZ9cnrTZxzg5xz7Z1z7WvXrn1UgSUCOEfXpbOY3LQd6aVK+50mJHaWrcj8Y47jzJU/+R1FopyKaRE5JDnZa43Mau9IIIP3uYnL+Zp7eIl3uRWAmjXV3hFF1gDBV481JHerRn5jkoHfnHObnHMHgC+BM0OYVSLF3LnU27WF8c07+J0kpKY2acsp65dQIX2v31EkiqmYFhEAWrU6fEMwxxvcQW8+5hGe4RXuOfSMVu+IKrOAFmbWzMzK4F1AOOywMcOAGwKrenQCtjvn1uO1d3QyswpmZkASsDic4cUnI0aQifFd8/Z+JwmpaU3aUjozg46rF/odRaKYimkRISUFFi0KPuJ4kfv4M2/zFAN4lkcOPaP2jujinDsI3AWMwSuEhzjnFprZHWaWta/lKGA5sBR4C+gfOHcG8AXwAzAf7/+MQeH9DMQXI0Ywr97xbK5Y3e8kITWnwYnsTyzFGavU6iHFpwsQRSTXEnhP8X/cy8u8wH38nScPHVd7R3Ryzo3CK5iDj70RdN8Bd+Zz7uPA4yENKJFl40aYOZO0Lnm2x8eUfaXL8WP9Ezlz5Ty/o0gU08y0iORYAu8RnmEAzzCIP/MX/kfwtWlq7xCJAxMnAjClaTufg4THtCZtabVhOVX37vQ7ikQpFdMica5Bg+z79/ASzzCAwfSmHwMJLqSTktTeIRIXJk6EihVZULe530nCYlqTNiTg6LR6vt9RJEqpmBaJYw0awLrAug638jYvcR9fcjk38T6ZJALe6h79+kFqqo9BRSR8Jk6EM8/kYGJ8dILOq3c8u0uX4wwtkSfFFB//UkQkl+Tk7EL6Wj5mEH35lgu5lk/ICHxrqFkTNm/2MaSIhNfmzbBgAfTqBXHS9XAgsTSzGrais/qmpZg0My0Sh1JSspfBu4yv+JAbmMg5XMGXpFP20Dj1SIvEmSlTvNtzzvE3R5hNa9KGFltWU3vXVr+jSBRSMS0Sh2680bu9gNF8xjXMogOXMox9lD80Rj3SInFo4kQoVw46xPZmLYeb1qQtgJbIk2JRMS0SR1JSvB7ojAw4m4l8xeUspBUXMYpdVD40rn599UiLxKWJE6FTJyhb9shjY8iiOs3YXraithaXYlExLRInkpOhT2DZ2NOZzgh68BvNOJ+xbCN7YwYzWLvWp5Ai4p9t22Du3Lhr8QDITEhkeuPWWm9aikXFtEgcqF49u0e6LXP5lu5spA7JpLKZ2jnGfvSRDwFFxH9TpoBzcVlMA0xt0pbG2zfQcNvvfkeRKKNiWiSG9e/vzTRv2+Y9PpHFjKMbO6lMEmmsp36O8eqTFoljkyZBmTJem0ccyuqbVquHFJWKaZEYVb06DByY/fhYlpFGEhkkkkwqK2maY7yZ+qRF4trEidCxI5Qvf+SxMWhpzUZsqliNM1ep1UOKRsW0SIzJusgwazYaoCGrSSOJsuwnmVR+5fhc56m9QySO7dwJc+bA2Wf7ncQ/Zkxr3NabmXbO7zQSRVRMi8SQlJTsiwyz1OV30kiiOn9wPmNZyMk5nk9MhMGD1d4hEtemTfOW+YnTfuks05q0oc7uP2i+ZY3fUSSKaAdEkRhy0005H9dgC+PoRgPWcj5j+YHTcjzfsiUsXBi+fCISoSZO9H6yPvNMv5P4amqgb7rzyrksq9XI5zQSLTQzLRIjUlLg4MHsx1XYzhguoAW/cinDmEbnHOP79VMhLSIBkyZB+/ZQqZLfSXy1ptoxrK5alzO1eYsUgWamRWJE8Kx0BXYzkotpyzwu42vGk3Toufr1tY60iATZswdmzoT77/c7SUSY1rgNF/z6PQmZGWQmJPodR6JAyGamzexdM9toZguCjj1hZmvNbG7g46JQvb9IPKlePXtWuiz7+JrLOIPvuY6PGcXFh8b166dCWkQOM306HDgQ9/3SWaY1aUO1fbs4aeNvfkeRKBHKmen3gVeBDw87/oJz7vkQvq9IXKlePXvljtKk8zlX0Y1UbuR9vuCqQ+N0cbqI5GniREhIgM6djzw2DnzfuA3grTe98JjjfE4j0SBkM9POuUnA1lC9voh4W4RnFdIJZDCYPlzCCPrxOh9y46Fxgwf7k09EosCkSXDKKVC1qt9JIsLGyjVZWqOh1puWQvPjAsS7zOynQBtI9fwGmVlfM5ttZrM3bdoUznwiUaFVq+wtwo1M3uFWruZz/sp/eIN+h8aVKaNl70QkH/v3e20eavHIYWrTtnRcvZDSGQf8jiJRINzF9ECgOXAKsB74b34DnXODnHPtnXPta9euHaZ4ItGhQQNYtCjrkeMV7uYmPuBxnuC//DXH2HffDXs8EYkWM2fCvn0qpg8zrXFbKh7YR5v1v/odRaJAWItp59wG51yGcy4TeAvoGM73F4kFycmwbl3WI8dzPMSdvM6/eZB/8liOsUlJmpUWkQJMnOjddunib44IM6PxyWRinLlSrR5yZGEtps2sXtDDy4EF+Y0Vkdz6989u7QB4jH/yN/7Da/TnIZ4D7NBzSUmQmhr+jCISRSZOhNatoUYNv5NElG3lq7Co7rFab1oKJZRL430CfA+cYGZrzOxW4N9mNt/MfgLOA7SopUgh9e8PAwdmP36A5/kHT/A+N3I3rxBcSLdsqUJaRI7gwAFvG3G1eORpWuM2nLp2Mezd63cUiXAhWxrPOXdtHoffCdX7icSylJSchfQdDOR5HmQIV3Ebb+OCfi4uX147G4pIIcyZ423YomI6T9OatKHvrK9g6lSvv04kH9pOXCQK9OmTff8GPmAg/RlOD/owmIygn4mrVfP+bxQROaKsfumzz/Y3R4Sa1bAVBxISYfx4v6NIhFMxLRLhGjTIvn8ln/Mut5BKElfxOQcoc+i5+vXhjz98CCgi0WniRDjpJKhTx+8kEWl32QrMq3e8imk5IhXTIhEseOWOixnBx1zH95xBT75hP+UOjStfXtuEi0gRHDwIU6ZoVvoIZjZq5bXD7N7tdxSJYCqmRSJUSkr2yh1dSeMLrmQebbmYkeyh4qFxpUurtUNEimjePNi5U/3SRzCzYSvvB48ZM/yOIhFMxbRIhLoxsBv4mUxlGJfyKy24gDHsIHvL34QESE/3KaCIRK+sfmkV0wX6ocFJYObN4ovkQ8W0SARq1QoyMuBU5jCKi1hDQ7oxjq3UzDEuI8OngCIS3SZOhOOO8y62kHztKFfJW4d78mS/o0gEUzEtEmH69/e2Cm/FAsZyPn9QnWRS2cAxOcYlJfkUUESiW2amVxxqVrpwunSB77/32j1E8qBiWiSCZK0n3YJfSCWZfZQjiTTW0CjHuGrVtCmLiBTT/Pne0j+6+LBwunTxLkD88Ue/k0iEKtKmLWaWAFRyzu0IUR6RuFWhgrfRVhNWkEYSiWRwHt+xnOa5xmoJPBEptkmTvFvNTBdOly7e7eTJ0KGDv1kkIh1xZtrMPjazKmZWEVgELDGzB0MfTSR+mHmFdD3WkUYSldhFN8bxMyflGtuvnw8BRSR2TJwITZp4H3Jk9evDsceqb1ryVZg2j5aBmejLgFFAY+D6UIYSiSeJid5tLTaRSjJ12Eh3vmUep+QaW60avP56WOOJSCxxzpuZ1qx00XTp4q3o4ZzfSSQCFaaYLm1mpfGK6W+ccwcA/W0SKQFm3rVA1fiDsZxPM36jByOYQadcY0uXVnuHiBylxYth0yYV00V11lmweTMsWeJ3EolAhSmm3wRWABWBSWbWBFDPtMhRMvNuK7GTUVxEKxZyOV8xibz/k9N60iJy1LLWl9bFh0UT3DctcpgjFtPOuZedcw2ccxc5z0rgvDBkE4lZWa0d5djLMC6lA7O4hs8Yw4V5jtdvFkWkREya5PUAN899YbMU4PjjoU4dFdOSp8JcgFjXzN4xs28Dj1sCN4Y8mUiMatDAa+0ow36+5ArOYSI38CFfc3musdWqqZAWkRLinDczfc452b8ak8Ix81o9VExLHgqzNN77wHvAgMDjX4DPgHdClEkkZiUnw7p1kMhBPuFaujOa23iLT7gu19ikJK0lLSIlaOlSWL+eR7fW4OOHR/qdJvp06QJffglr1kDDhn6nkQhSmJ7pWs65IUAmgHPuIKBNjEWKKDkZ0tIggQze5yau4Cvu5UXe4bZcY1u2VCEtIiUs0C89o9HJPgeJUll901Om+JtDIk5hiundZlaTwAoeZtYJ2B7SVCIxxswrpMExkH70IYVHeZqXuTfX2KQkWLgw7BFFJNZNnMimCtVYVkOzqsXSti1UqqRWD8mlMG0efwGGAc3NbCpQG7gypKlEYkh2a6Ljf/yFvrzF0zzKv3g019h+/bSOtIiEyKRJzGzUSv3SxVWqFJxxhoppyaUwq3n8AJwDnAncDrRyzv0U6mAisSD4/6wn+Tv38yIvcQ//x1O5xtavr0JaREJkxQpYtUotHkerSxdYsECL/ksOR5yZNrMbDjt0qpnhnPswRJlEYkJwIf0w/+L/eJq3uI37eBHIPTO0dm3YoolIvJk0CYCZKqaPTpcu3qooU6dCjx5+p5EIUZg2jw5B98sBScAPgIppkXyUKZN9/25e5l88SgrXcQdvkFchreXvRCSkJk+GatVYUruJ30mi2+mne9vRTp6sYloOOWIx7Zy7O/ixmVUFPgpZIpEol5wMBw5492/hHV7mXr7iMm7ifTJJzDVehbSIhNzkyXDWWTgrzLoDkq/y5aF9e63oITkU51/VHqBFSQcRiRXeqh3Qi094iz8zmgvoxaccpHSOcfXrq5AWkTDYuBGWLMle2k2OTpcuMGsW7N3rdxKJEIXZAXG4mQ0LfIwAlgDfhD6aSPTJ6pPuydd8xPVMpgtX8CXplM0xLilJPdIiEiZZq0+omC4ZZ53l/fpx5ky/k0iEKMzM9PPAfwMf/wLOds49HNJUIlGmf//sQvp8xvAZ1zCb9vRgBHupkGNstWrakEXCy8wuNLMlZrbUzHJ9/zbPy4HnfzKzU4Oeq2ZmX5jZz2a22MzOCG96OWqTJ3vtCaed5neS2NC5s3erJfIkoDA90xPDEUQkWvXvDwMHeve7MImvuJzFnER3vmUXlXOMrV9fM9ISXmaWCLwGdAPWALPMbJhzblHQsO547XstgNOBgYFbgJeA0c65K82sDBz206FEvsmToVOnnFdGS/HVqAEnn6xiWg7Jd2bazHaa2Y48Pnaa2Y5whhSJZFmFdAdmMpKLWUkTzmcs26ieY1zp0iqkxRcdgaXOueXOuXTgU6DnYWN6Ah86z3SgmpnVM7MqwNnAOwDOuXTn3LYwZpejtWMHzJ2rFo+S1qULTJsGBw/6nUQiQL7FtHOusnOuSh4flZ1zVcIZUiRSZbV2tGEeY7iAjdQhmVQ2USfX2PT0MIcT8TQAVgc9XhM4VpgxxwKbgPfM7Ecze9vMKoYyrJSwadMgM1PFdEnr0gV27YKftIedFGE1DzOrY2aNsz5CGUokGmQV0ifwM+Poxi4qkUQa63LVKd424SI+yWvv6MPXkclvTCngVGCgc64dsBvI85oZM+trZrPNbPamTZuOJq+UpMmTs7fBlpKT9cOJWj2Ewq3mcamZ/Qr8BkwEVgDfhjiXSMRq1Sq7kG7GctJIIpMEkkhjJU1zjW/ZUtuEi6/WAI2CHjcE1hVyzBpgjXNuRuD4F3jFdS7OuUHOufbOufa1a9cukeBSAiZPhlNPhYr6hUKJatgQmjRRMS1A4WamnwQ6Ab8455rh7YA4NaSpRCKUGSwKXLbVkNWkkUQ59tGNcfzK8bnG9+sHCxeGOaRITrOAFmbWLHABYS9g2GFjhgE3BFb16ARsd86td879Dqw2sxMC45KARUh02LcPZsxQi0eodOniFdPaMCDuFaaYPuCc2wIkmFmCc+474JTQxhKJPBb0i/A6bCCVZGqwlQsYwwJa5xo/eLBmpMV/zrmDwF3AGGAxMMQ5t9DM7jCzOwLDRgHLgaXAW0D/oJe4G0gxs5/wvvc/E67scpRmzfIu1lAxHRpdungb4vz6q99JxGdHXBoP2GZmlYBJeN9QNwK6fFXiSqtW2fdrsIVxdKMha7iAMcyhfa7xSUnQu3cYA4oUwDk3Cq9gDj72RtB9B9yZz7lzIY+/5BL5sloQzjrL3xyxKrhv+vjcv5mU+FHQ0nhXmlk5vCWT9gD3A6OBZcAl4YknEhmyWjsqs4PRXMjx/EJPvmEquf+Tql9fm7KISASYPNmbCahZ0+8ksenEE6FWLZgyxe8k4rOC2jx6A6vwFu+/AG/y4gPn3MuBtg+RuJDV3lGB3YzkYk5hLlfxOWkk5xrbsqXWkhaRCJCRAVOnqsUjlMy8WX9dhBj3Clpn+nLgOCANuAfvIpSBZnZ2uMKJ+C0x0bstyz6+5jLOZBq9SWFEHr+cGTxYFxuKSISYNw927oSz9V92SHXpAsuWwfr1ficRHxV4AaJzbkdgNro70BqYC7xiZqsLOk8kFrRq5e11UIoDDOFqupHKrbzD51ydY1z58t7F3OqRFpGIkTVbqpnp0MrqR9fsdFwr1KYtZlYduAK4BqgBDA1lKJFIsGgRJJDBR1zPpQynP6/xATflGFO+POzZ408+EZF8TZ4MTZt66yFL6LRrBxUqqJiOc/mu5mFmlYHLgGvxFukfBjwFfBe48lskZlWoAEYmb3MbvfiMB/k3A3OsFuZRIS0iEcc5mDQJLrzQ7ySxr3Rpb3dJFdNxraCZ6d+AC/EuQGzknOvrnBuvQlpinRns3et4mXu4mfd5gsd5ngdzjUtK8iGciMiR/PILbNqkfulw6dIFfvoJtm/3O4n4pKB1phs75zTvJnHFW7nD8SwPcxev8TwP8A8ezzWufHktfyciEUr90uHVpYv324Bp06B7d7/TiA8KWs1DhbTElawl8P6Pp3iIfzOQO3iQ/wCWa6zaO0QkYk2aBHXqaCORcDn9dChVSq0ecaxQFyCKxLKUlOxC+n7+x5M8xgfcwJ28Rl6F9ODB4c0nIlIkkyd7q0xY7u9fEgIVK8Kpp6qYjmOF2U5cJGalpECfPt7923mD//EAQ7iKW3kHl8fPmhUragk8EYlga9bAihVw331+J4kZTR8eecQxj7oG3Pj9cMru2wflyoUhlUSSglbzGA7ke7Ghc+7SkCQSCZMyZeDAAe9+Hz7idfozgovpw2Ay8vmn8eabYQwoIlJU6pf2xaxGreg76yuYNUt/9nGooDaP54H/4q3qsRd4K/CxC1hwpBc2s3fNbKOZLQg6VsPMxpnZr4Hb6kcXX6R4zLIL6SsYyvvcxHecx5V8wQHK5HnO4MGalRaRCDdpElSuDG3b+p0krsxq2NK7M2WKv0HEF/nOTDvnJgKY2ZPOueD1dYab2aRCvPb7wKvAh0HHHgbSnHPPmtnDgccPFTm1yFEIbiPszig+4Vqm04mefMN+cv96rmVLbRMuIpHp8BaEMV+MYn2t47lpwGifEsWnbeWr8EvNxhw/eTI88ojfcSTMCnMBYm0zOzbrgZk1A2of6STn3CRg62GHewIfBO5/gLcpjEhYBF9oCHAe4/mSK5hPay5iFLuplOuc0qVVSItIdKi2dwcnbF7FzEat/I4Sl2Y2auXNTB886HcUCbPCFNP3AxPMbIKZTQC+A+4r5vvVdc6tBwjc1slvoJn1NbPZZjZ706ZNxXw7EU/whYYAZzCNYVzKUo7jAsawg6q5zmnZEtLTwxhSROQotF+zGAhqOZCwmt64NezcCT/+6HcUCbMjrubhnBttZi2AEwOHfnbO7Q9tLHDODQIGAbRv3167LspRCS6k2/ED39Kd9dQjmVS2UCvXeO3zKSLRpuPqBexPLMVP9bS+tB9mNGrt3ZkwATp08DWLhNcRZ6bNrALwIHCXc24e0NjMehTz/TaYWb3A69YDNhbzdUQKLbi1oyULGcv5bKMaSaSxgWNyjVchLSLRqOOahcytdwL7S+V9EbWE1qZK1eHEE71iWuJKYdo83gPSgTMCj9cATxXz/YYBNwbu3wh8U8zXESmU4EL6OH4llWTSKUMSaaymcY6x/fqpkBaR6FQhfS+tNixjlvql/XXuud7yhOqbjiuFKaabO+f+DRwAcM7tJa9t4Q5jZp8A3wMnmNkaM7sVeBboZma/At0Cj0VColXQ/ymNWUkaSZTiIMmksozjcoxt2RJefz3MAUVESki7dUsonZnBrIYqpn113nle3/QPP/idRMKoMDsgpptZeQIbuJhZc+CIPdPOuWvzeSqp8PFEim/RIu/2GNaTRhKV2UlXxrOYnBfnJCVBaqoPAUVESkjH1QvJsATmNDjJ7yjx7ZxzvNsJE6BjR1+jSPgUZmb6cWA00MjMUoA04G8hTSVylLLaO2qxiVSSOYbf6c63zKVdjnH9+qmQFpHo12HNQhbVacaushX8jhLf6taFk06C777zO4mEUYHFtJklANWBK4CbgE+A9s65CSFPJlJMWe0dVdnGGC7gWJbTgxHMoFOOcdWqqbVDRKJf6YwDtFu3RC0ekeK887z1prO22ZWYV2Ax7ZzLxFvFY4tzbqRzboRzbnOYsokUy6JFUJFdjOIiTmYBV/AlEzk3x5jy5eGPP/zJJyJSklr/vpTyB/drs5ZIce65sGuX+qbjSGHaPMaZ2V/NrJGZ1cj6CHkykSJKTvbaO8qxl2FcSkdm0otPGU33XGP37PEhoIhICHRY423TqpnpCBHcNy1xoTAXIN4SuL0z6JgDjs1jrIgvKlSAvXuhNOkM5U+cywSu5yO+4opcYwcP9iGgiEiIdFi9kGU1GrKlYjW/owhAnTreElHffQcPPeR3GgmDwuyA2CwcQUSKq0wZrzUtkYN8zHVcxLf8mUF8TO9cY5OSoHfuwyIiUclcJh3WLGLUCZ39jiLBzjsP3n/f+8+pdGm/00iIFWoHRDP7PzMbFHjc4ih2QBQpUdWre9+rjEze42auZCj38QJv8+c8x2vlDhGJJSdsWknV/bu1WUukOfdc2L0b5szxO4mEQVF2QDwz8PhodkAUKTH9+8O2bQCO1+nP9QxmAE/xEvflOb5fvzCGExEJg6x+6ZmNTvY5ieRw9tnerZbIiwsh2wFRJNQGDgRw/JcHuIM3+RcP8wyP5jm2Xz8tgycisafj6oWsq1yLNVXq+B1FgtWp463TqosQ40LIdkAUCaX+/b3bf/A4f+EFXuZuHuUZ8vo5z7nwZhMRCQvn6LBmITMatc7eqUoix3nnwbvvqm86DmgHRIlKAwfC33iOx3iSd7iF+3gRFdIiEleWL+eYXVu1vnSkOvdcbx3W2bP9TiIhVpjVPMaZ2Q9AJ7xq5V5t3CJ+MoM7eZXneJiPuZa+DMId9nNhQgJkZPgUUEQkHAL9uDPULx2Zstab/u47OOMMf7NISOU7M21mp2Z9AE2A9cA6oHHgmEjYmcHNvMur3M3X9ORGPiCTxFzjVEiLSMxLS2NDpRosrdnI7ySSl1q1oHVr9U3HgYJmpv8buC0HtAfm4c1MtwFmAGeFNppItpQU6NMHruFT3uY2xnA+1/AZB8ndh9aypQ8BRUTCKTMT0tKY0qSt+qUj2bnnwjvvQHq6tymCxKR8Z6adc+c5584DVgKnOufaO+dOA9oBS8MVUCSrkL6EYXzE9UzhLC7nK9Ipm+f4hQvDHFBEJNzmz4dNm5ja9BS/k0hB1DcdFwqzmseJzrn5WQ+ccwvM7JTQRRLJ1qABrFsH3RjL51zFD5xKD0awlwp5jtdW4SISFwI7UE1t0tbnIFKg4PWmzzyz4LEStQqzmsfPZva2mZ1rZueY2VvA4lAHEzHzCumzmMzXXMbPnEh3vmUnVfIcP3iwtgoXkTiRlgYnnsiGyrX8TiIFqVUL2rRR33SMK0wxfROwELgXuA9YBNwcukgi2S2AHZjJSC5mFY3pxjj+oEae4/v1UyEtInEiPR0mToTkZL+TSGGcey5Mnep93SQmFdjmYWaJwAjnXDLwQngiSTyrXj1ri3BozU+M5kI2U4sk0thE3jt8JSVpd0MRiSPTp3t9uMnJ8L3fYSRY04dH5jp2wepKvLl3L1fe8iKzG2avCb7i2YvDGU1CqMCZaedcBrDHzKqGKY/EMbPsQvoEfmYc3dhDBZJIYx0N8jxn8OBDrYMiIvEhNdVbTD9rHWOJaDManUwmRqdV8488WKJSYdo89gHzzewdM3s56yPUwSS+BK/s1JTfSMX79WUSaaygWZ7nqLVDROJSWhp06ADVqvmdRAphW/kq/FynqYrpGFaY1TxGBj5EQiIxaM+VBqwhjSQqsIdzmcAvnJDnOf36qbVDROLQjh0wYwY8/LDfSaQIpjdqzbXzxlDm4AHSS+XeH0GiW2GK6c+A4wAHLHPO7QttJIknFSp4ew8A1GEDqSRTi80kkcZ82uQa37Kl1pEWkTg2caK3xasuPowq0xu35pY5w2i7fgmztP17zMm3mDazUsAzwC14G7ckAA3N7D1ggHPuQHgiSqxq1Qr27vXuV2crYzmfxqziAsYwmw65xmvpOxGJB3ldxJbl8dS36FWqLG1HbCN9tH5pHC2C+6ZVTMeegnqm/wPUAJo5505zzrUDmgPVgOfDkE1iWEoKLFrk3a/MDkZzISfyMz35hil0yTXeORXSIiKdV8xjVsOWahWIMtvLV2ZxnWZ0Wq2+6VhUUDHdA/izc25n1gHn3A6gH3BRqINJ7EpO9rYHB6jAbkbQg3b8yFV8TirdcoxNSvIKaRGReFd711aO37KKKdpCPCpNb9ya09b+TJmD+sV+rCmomHbO5S5jAsvlqbyRYilTxrsQHaAM+/mKy+nMVPowmOFcmmNsUpKWvRMRydJ55TwApqqYjkrTG7em3MF0Tlm/xO8oUsIKKqYXmdkNhx80sz7Az6GLJLGqTBk4EPiBvBQHGMLVnM84buNthnBNjrHVqqmQFhEJdtaKuWwtX4VFdfJeLlQim9abjl0FreZxJ/Clmd0CzMGbje4AlAcuD0M2iSENGmQX0glk8CE30JNh3MmrvH/Y7vSlS8Mff/gQUkQkUjlH5xVzmda4Dc4Ks0WERJod5SqxqO6xdFo1n5c7X+t3HClB+RbTzrm1wOlm1hVoBRjwrXMuLVzhJDYEbxFuZDKIvlzLp/yN53idO3ONT08Pbz4RkUh37Na11Nu1RS0eUW56o5O5/sdRlD2o/+hiyRF/vHXOjXfOveKce1mFtBRVq1bZhTQ4XuQ+buVd/snf+Q9/yzVeFxuKlDwzu9DMlpjZUjPLtduHeV4OPP+TmZ162POJZvajmY0IX2oJ1nnlXABdfBjlpjduQ9mMA5yyTn3TsUS/K5KQylr+DhzP8Cj38Ar/5S88zj9yjVUhLVLyzCwReA3oDrQErjWzlocN6w60CHz0BQYe9vy9wOIQR5UCnLViLqur1mV1tWP8jiJHYWajVuqbjkEqpiVkKlTIvj+Ap3mEZxnIHfyV5/G6hjz166uQFgmhjsBS59xy51w68CnQ87AxPYEPnWc6UM3M6gGYWUPgYuDtcIaWbImZGZyxaj5TmrT1O4ocpR3lKrGw7rGcseonv6NICVIxLSHRoEH27ob38QJP8Xc+5Hru5DWCC+lq1WDtWl8iisSLBsDqoMdrAscKO+ZF4G9AZkFvYmZ9zWy2mc3etGnTUQWWnE7+fSlV9u9Wv3SMmN64Ne3WLYF9+/yOIiVExbSUuDJlYN067/6fGcQL/IUv+BO38C4u6K+cVu0QCQvL49jhvwvKc4yZ9QA2OufmHOlNnHODnHPtnXPta9euXZycko+s9aWnaWY6Jnwf6Jtm+nS/o0gJUTEtJcosewm83gzmDe5gJBdxHR+TEbR4TLVqWrVDJEzWAI2CHjcE1hVyTGfgUjNbgdce0tXMBocuquTlrBVzWVSnGVsrVPU7ipSA2Q1bkmEJMGGC31GkhKiYlhKRkuIV0lku50ve5yYmcC5X8gUHKJNjvGakRcJmFtDCzJqZWRmgFzDssDHDgBsCq3p0ArY759Y75x5xzjV0zjUNnDfeOdcnrOnjXLkD+zht7SKmNDnF7yhSQrL6pvnuO7+jSAlRMS1HLSUF+gT999qdUXxKL2bSkUsZxj7K5xjfr1+YA4rEMefcQeAuYAzeihxDnHMLzewOM7sjMGwUsBxYCrwF9PclrOTSfs1iymYcVL90jJnWuA18/z3s3Ol3FCkBBe2AKFIo11+fff9cvmMof2I+rbmIUeymUo6x9evD66+HOaBInHPOjcIrmIOPvRF030EeOyjlHD8BmBCCeFKAs1bOJT2hFDMbtvI7ipSg75p34I6ZX8K4cXDFFX7HkaOkmWk5KtWrZy9r14nvGc4lLOdYLmAM26mWY2z58lq5Q0SkKDqvmMuPDU5kb5lyfkeREjSnwUnexUMjtA9SLFAxLcVWoUL27oan8CPf0p311COZVLZQK8fYli1hz57wZxQRiVbV9u6g1YblWl86Bh1MLAUXXACjRkFmgatOShRQm4cUS5ky2at2nMQixnI+26lKEmn8Tr0cY/v1U2uHiEhRnbHyJxJw6peOUfftbsiLGzZw6c0v8VO94wscu+LZi8OUSopDM9NSJFmrdmQV0s1ZSirJHKQUSaSxmsY5xquQFhEpnrNWzmVnmfLMO0KhJdFpYrNTybAEkpbO8juKHCUV01Joh6/a0YhVpJFEGdJJJpVlHJdjvHMqpEVEiqvzinlMb9yajIREv6NICPxRoSo/1D+Rrstm+h1FjpKKaSm0227Lvn8M60kjiaps53zGsoicV5onJYU5nIhIDGm47XeablvPVK0vHdPGH9eB1huWUXfnZr+jyFFQMS2FkpIC+/Z592uymXF0ox7r6c63/MipOcbWrw+pqT6EFBGJEVlbiE9Rv3RMS2veAYDzls32OYkcDV+KaTNbYWbzzWyumelvUIQLbu+oyjbGcAHNWcYlDGc6Z+QYm5Sk5e9ERI5W55Xz2FCpBktrNjryYIlav9RqwpoqdUhapr7paObnzPR5zrlTnHPtfcwgBUhJgYSE7EK6IrsYycW0Zj5/YigTOC/H+MGDNSMtInK0zGVy5sp5TG3S1rviW2KXGeObd6DzyrmUPZjudxopJrV5SJ6yZqOzNmQpx16+oSedmM61fMK3XJRjvHPQu7cPQUVEYsyJm1ZQa8929UvHifHNO1DhwH46rZrvdxQpJr+KaQeMNbM5ZtbXpwxSgBtvzL5fmnS+4ErO4ztu5AO+5E85xvbrF+ZwIiIxrPOKuQDezLTEvO+btGFP6bJa1SOK+VVMd3bOnQp0B+40s7MPH2Bmfc1stpnN3rRpU/gTxqn+/b3fKmZkeI8TOUgKvbmYUfRjICn0yTE+MVHL34mIlKTOK+exrEZDfq9S68iDJertL1WGqU1O8dabzvp1sEQVX4pp59y6wO1G4CugYx5jBjnn2jvn2teuXTvcEeNS//4wcGD2YyOTd7mFq/iC+/kfg7g91zkffBDGgCIisS49ndNXL2BKU81Kx5O05h1ouGMjx29e6XcUKYawF9NmVtHMKmfdB84HFoQ7h+QWXEiD4zXu5AY+4u/8kxe5P9f4wYPVJy0iUqK+/54KB/arXzrOfNfcW4tBq3pEJz9mpusCU8xsHjATGOmcG+1DDgnSKseeK47/8CD9eINneYin+L8cY5OSdMGhiEhIfPMN+xNL8X2TNn4nkTDaULkW8+s2p6u2Fo9KpcL9hs655YB+fxVBkpNh0aLsx0/wBH/lv7zCXTzCv4DspZnUziUiEiLOwdChTGnajp1lK/qdRsJsfPMO3PX9EKrt3cG28lX8jiNFoKXx4lyDBpCWlv34Qf7N4/yTd7mZe3mJ4EJaq3aIiITQ7NmwahWjjz/T7yTig/HNO5DoMjln+Ry/o0gRqZiOYw0awLp12Y/78xr/5iE+5Rr+zFu4oL8e/fpp1Q4RkZAaOhRKlWJsi05+JxEf/FSvBZsqVFPfdBRSMR2n+vfPWUjfyPu8xl18w6Vcz0dkknjoORXSIiIhFmjx4Lzz2F6+st9pxAfOEviueXvOWT6HUhkH/Y4jRaBiOk4Fr9xxNZ/xDrcylm5cw2ccpPSh55KSVEiLiITc/PmwdCn86U9HHisxK615R6ru381paxf7HUWKQMV0nElO9jZlydKD4QymD1PpzGV8zX7KHXouKQlSU30IKSISb4YO9b45X3aZ30nER1OankJ6Qim6qtUjqqiYjhMpKd736eCLDZNI5Quu5Efa0YMR7KVC9nMqpEVEwueLL6BLF6hb1+8k4qPdZSswvXFrkpZqa/FoomI6xqWkQKlS0CfnLuB0Zgrf0JMlnMCFjGYn2cvwDB6sQlpEJGx+/tlbn1QtHoK3gctxW9fQ+I/1fkeRQlIxHcNSUrwiOiMj5/HTmM0oLmI1jejGOP6gxqHn+vXTZiwiImE1dKh3e8UV/uaQiJDWvCOAWj2iiIrpGDZgQO5jJzOfMVzAFmqSTCobyf6VYv36uthQRCTshg6FTp2gYUO/k0gEWFW9HktrNFQxHUVUTMewlStzPm7BL6SSzF7Kk0Qaa8n+xl2/PqxdG+aAIiLxbvly+PFHtXhIDmnHdaTTqvlU3L/H7yhSCCqmY1SrVjkfN2EFaSRhOJJJ5TeOPfRcv34qpEVEfPHll96timkJMr55B8pkHuSsFXP9jiKFoGI6BqWkeNeyZKnPWsbTlYrsJplUlnAiAC1bevsEqLVDRMQnX3wB7dpBs2Z+J5EIMqfBSWwvW5GkZVrVIxqomI5Bt92Wfb82G0klmVps5kJGM582gLdix8KFPgUUERFYswZmzIArr/Q7iUSYg4mlmHjsaZy3fDbmMv2OI0egYjqG9O/vrSW9b5/3uDpbGcv5NGElPRjBLLwrhAcP1oodIiK+U4uHFGB88w7U3r2N1r8v9TuKHEEpvwNIyWjVKmdrRyV28i3dOYnFXMJwJnM24LV2qJAWEQmvpg+PzHXss4/folqtxlzw3lJABZPkNLHZqWRYAklLtapHpNPMdAzo3z9nIV2ePYygB6cxh6sZwjjOByAxUa0dIiKRoNbuP+iweiGjj+/sdxSJUH9UqMoP9U+kq/qmI56K6RjwxhvZ98uwn6+4nC5Mpg+DGUbPQ8998IEP4UREJJcLfvmeBBzfnnCm31Ekgo0/rgOtNyzTklsRTsV0lOvf31uRA6AUB/iMa7iAsdzG23xGr0PjkpLU3iEiEikuXDKN5dXr83Ptpn5HkQiW1ryDd2fUKH+DSIFUTEexlBQYONC7n0AGH3Ajl/ENd/My73HLoXEtW0Jqqk8hRUQkh2p7d3DGqp8YfcKZ3lXjIvn4pVYT1lSpAyNG+B1FCqBiOkqlpMCNN3r3jUze5Hau4xMe5l+8yt2HxvXrpz5pEZFI0u3XGZRymXyrfmk5EjPSjuvgzYjt2uV3GsmHiukoddttkJEB4HiB+7mNd3iS/+M5Hj40RhuyiIhEngt/mcaaKnWYf8xxfkeRKPDNSefCnj0wZIjfUSQfKqajTEoKlC2bvZb00wzgXl7mf9zPY/zz0Lh+/XwKKCIi+aq8fzdnrfiR0cefoRYPKZQfGpwIJ5wA77zjdxTJh4rpKJGSApUqQZ8+kJ7uHXuEZ3iUf/EmfXmA/wLeN+aKFTUjLSISibounUnZjIOMOuEsv6NItDCDW2+FadPg55/9TiN5UDEdwVJSoFYt799Rnz6we3f2c/fyIs8wgI/oQz8GklVIA7z5ZviziojIkXX/ZRq/V6rBjw1O8DuKRJMbbvA2i3j3Xb+TSB5UTEeo/v29AnrLltzP3cZbvMj9DOUKbuY9XNCXsV8/LYEnIhKJyqfv45zlPzDm+DNwpv9+pQjq1oUePbwNIw4c8DuNHEb/miNMVjtH1pJ3h7uOFN7kdkbRnWv5hIygHeGTktTeISISqc5dPpvyB/dr10MpnltvhY0bteZ0BFIxHUFSUuDmm3O2cwS7jK/4gBuZyDn8iaEcoMyh55KStJa0iEgk6/7LNLaUr8LMRq38jiLRqHt3OOYYXYgYgVRMR5B7783/tzcXMJrPuIZZdOBShrGP8oee69dPhbSISCQrezCdrstmMeb4M8hISPQ7jkSjUqW8DSZGjYL16/1OI0FUTEeI/v3z7o8GOIcJfMXlLKQV3fmWXVQGoGZNGDxYrR0iIpGuy28/Uil9L6OPP9PvKBLNbrnF22Tiww/9TiJBVExHgP798++RPp3pjKAHyzmW8xnLzoRq9OvnbciyebMuNhQRiQbdf5nK9rIV+b5JG7+jSDQ7/ng46yxvVQ/n/E4jASqmfZaSAm+8kfdzbZnLt3Tnd47hoxtS2eRqk5GhmWgRkaiSnk7yrzNIbXE6BxJL+51Got2tt8Ivv8DUqX4nkQAV0z679968f7g8kcWMoxs7qcyCF9N49oN64Q8nIiJHb/x4qu7fzbdaxUNKwlVXect+6ULEiKFi2idZG7Lk1Sd9LMtII4mDlGLu82lcdm+T8AcUEZGSMXAgW8pXYXKzdn4nkVhQsSL06gVDhsCOHX6nEVRM+yIlBfr2zbuQbsQq0kiiDOm8ffU4Ln2gRfgDiohIyVi6FIYPZ3C7i9hfqsyRx4sUxq23wp49XkEtvlMx7YMBA7x/A4ery++kkkx1/uCtK8fw989ODn84EREpOa+8AqVKMbjdRX4nkVhy+unQsqVaPSKEimkfrFyZ+1gNtjCObjRgLb2qfMsjn58W/mAiEpPM7EIzW2JmS83s4TyeNzN7OfD8T2Z2auB4IzP7zswWm9lCM7s3/Omj2Pbt3qoLvXqxqVINv9NILDHzlsmbPh0WLfI7TdxTMR1m/fvnPlaF7YzhAlrwK1eXHUaf17UOqYiUDDNLBF4DugMtgWvNrOVhw7oDLQIffYGsxToPAg84504COgF35nGu5Ofdd2HXLu9Kc5GSdv313kYu777rd5K4V8rvAPEkr2XwKrCbkVxMG37ixspfcd3AJK0dLSIlqSOw1Dm3HMDMPgV6AsHTWT2BD51zDphuZtXMrJ5zbj2wHsA5t9PMFgMNDjs3bjV9eGS+zyVkZjBx0HOsa9iKaz7/PYypJBbl93dt4LEd6TDwbc6wsw4tu7ji2YvDGU3QzHTYpKR4u4AGL4NXln18Q0/O4Huu42M+2XGxCmkRKWkNgNVBj9cEjhVpjJk1BdoBM/J6EzPra2azzWz2pk2bjjZz1Ov26wwabd/Au+17+h1FYtiQNt2otWc7XZfO8jtKXFMxHWJZS+D16ePtAJqlNOl8wZUkk8bNvMfsJlf6F1JEYpnlcezw1e0LHGNmlYChwH3OuTzX4nLODXLOtXfOta9du3axw8aKW2Z/w+qqdRnX4nS/o0gMm9TsVH6vVIOr54/zO0pcUzEdQvktgZfIQQbThx6M5A4GMthu4Omn/ckoIjFvDdAo6HFDYF1hx5hZabxCOsU592UIc8aMk39fyulrFvL+qT3ITEj0O47EsIyERIaenMS5y+dQd+dmv+PELRXTIZTXEnhGJm9zG1fzOQ/wPIPsDu64A7V3iEiozAJamFkzMysD9AKGHTZmGHBDYFWPTsB259x6MzPgHWCxc+5/4Y0dvW6e/Q27ypRnSNvz/Y4icWBIm24kukz+tGC831HilorpEFq16vAjjle5i5v4gMf4By8lPsBHH8Hrr/uRTkTigXPuIHAXMAZYDAxxzi00szvM7I7AsFHAcmAp8BaQte5QZ+B6oKuZzQ18aMHkAtTetZVLFk/m89bJ7Cxb0e84EgdWVq/P9EYnc/VP43JemCVho9U8Qqhx4+A1pR3/5m/0ZyDP8Tf+W/7vfPCWZqRFJPScc6PwCubgY28E3XfAnXmcN4W8+6klH31+HEWpzAzeP+0Sv6NIHBnSphv/G/kCp69eAPTwO07c0cx0CD39NFSo4N1/jH/yIM/zKnfynxrPMugtUyEtIhJDyh5Mp8+Po0g7riMrq9f3O47EkVEndGZHmQq6ENEnmpkOkZSU7J7pB+15/uGe4POKN1F94Mtsvl4TPSIisabnwgnU3LtDy+FJ2O0rXY7hLc/migXfeTtvVq3qd6S4opnpEha8FN7KldCP1/m3e5AvEq/mwMC36X29/shFRGKOc9wy+xsW127K941b+51G4tCQ1t0of3A/fPqp31Hiji+VnZldaGZLzGypmT3sR4ZQOHwpvBv4gNe5k2FcwrUZg3n071oiSUQkFp25ch4nbl7pzUqbfvso4Tev3vH8XKuJthf3QdiLaTNLBF4DugMtgWvNrGW4c4RC8FJ4V/I573IL40jmaoZwkNJ5rO4hIiKx4JbZ37C5QlWGtTzH7ygSr8z4tO0FMHMmTJjgd5q44sfMdEdgqXNuuXMuHfgUiPoGs5SU7JU7LmYEH3Md0ziTy/ia/ZQDvNU9REQktjTdupbkZbNIOeUi9pcq43cciWOftL0AGjWCBx+EzEy/48QNP4rpBsDqoMdrAsdyMLO+ZjbbzGZv2rQpbOGKI6u9AyCJVL7gSuZyCj0YwR68dUYrVEC7HIqIxKCb5gxnf2IpBrfTEtzir/2ly8JTT8Hs2TBkiN9x4oYfxXRezWS5Vhl3zg1yzrV3zrWvXbt2GGIVX1Z7x5lM5Rt68istuJDR7MC7mrZmTRg0SGtKi4jEmir7dnHV/FSGn3QOmypV9zuOiFdstG0Ljz4K+/f7nSYu+LE03hqgUdDjhsA6H3Ictazl71auhNOYzSguYg0NSSaVrdQEYPBgFdEiIrHq6p/GUvHAPt5rf6nfUUQAaDpgNF1O+BMfDXmMf150N+92yL+TdsWzF4cxWezyY2Z6FtDCzJqZWRmgFzDMhxxHJau1Y+VKaMUCxnABW6lBEmlspC4ATZqokBYRiVWJmRncNGcE0xudzMK6zf2OI3LI5GanMqlpO+6e9ilV9u3yO07MC3sx7Zw7CNwFjAEWA0OccwvDneNoZbV2tOAXUklmH+VIIo21NATUIy0iEuvO/+V7Gu7YqE1aJCI9e+7NVN23i37Tv/A7SszzZZ1p59wo59zxzrnmzrmoLDlXrYImrCCNJBLIJIk0fuNYwJuRVo+0iEhsu2X2MFZVrUvqcR39jiKSy6K6x/LVyedxy+xvqL9jo99xYpq24yum9vXXkUYSldhFN8axhBMBr5BesUKFtIhITJs1iw5rF/H+aZeSmaANuSQy/bdLHwAemDzY5ySxTcV0cWzaxDiXTB02ciGj+Ym2gFo7RETiQmYm/OUvbCtXiSFtuvmdRiRf66rU4b32l3L5gu9ouWG533FilorpIkhJgTaN/uDHOudTZv0K3u45gg1NTsdMrR0iInHjzTdhyhSe6nobu8pW8DuNSIFe73QV28tV4uEJ7/kdJWbFfTGdkgJNm0JCgnebkpL3c7VqwT0372TQmu60ZBGXua/4v3Hn8PTT3iSFWjtEROLAmjXw0EOQnMwXJyf5nUbkiHaUq8QrZ/bi7BU/0uW3H/yOE5PiupgOXt7OOe+2b1/v+OHP7dmyh6EHLqE9s7mGzxjLBezZ463qISIiccA56NcPMjK82WnLaw8ykcgzuN1FrKpal0cmvEdCZobfcWJOXBfTWcvbBcsqkIOfK8N+hvInzmYS1/MR33DZofGrVoUvr4iI+GjIEBgxAp58Eo491u80IoWWXqo0/zn7Blpu/I3LFk3wO07MietiOr9CeNWq7OcSOcgnXEt3RvNn3uJTrs0xtnHjEIcUERH/bdkCd98NHTrAvff6nUakyEac1IW59VrwwKTBlD2gbcZLUlwX0/kVwo0bex8JZPABN3IFX3EPL/Eut+YYp9U7RETixF/+An/8AW+/DYlaCk+ij7MEnj33Zhrs3MRNPwz3O05Mieti+umnvYI4WFaB/PRTjrcS+9Gbj3mEZ3iFeyhdGmrWRKt3iIjEkzFj4MMPvQsP27TxO41IsU1v3IbU5h248/vPqbZ3h99xYkZcF9O9e3sFcZMmhxXI1zl6z76fWzLe4pUqA3jOHqFJE3jvPdi8Wat3iIjEjV274Pbb4YQT4P/+z+80IkftuXNuomL6Xu6e9pnfUWJGKb8D+K137zyK4v/7O7z0Etx7L3e/8CR364JtEZH49Pe/e8s6TZ4M5cr5nUbkqP1auwlDWidz/Q8jYflyXUxbAuJ6ZjpP//qX1+dx223wwgta+khEJF7NmOFNrPTvD2ed5XcakRLzwlm9OZiYqPV9S4iK6WAvvwyPPgrXXQdvvKFCWkQkXqWne5MqDRp4kywiMWRj5Zq81eFy+PRT+PJLv+NEvbhv8zjknXe85Y4uvxw++EBXa4uIxLPnnoMFC2D4cKhSxe80IiXu9TOu5l63Evr0gUmToH37Asc3fXhkkV5/xbMXH028qKKZaYBPPoE//xkuvNC7X0o/Y4iIxK3Fi+Gpp6BXL+jRw+80IiGxv1QZ+PprqFsXLr0U1qzxO1LUisliOiUFmjaFhATvNiWlgMFffw3XXw9nnw1Dh0LZsuEJKSIikScz02vvqFTJ65cWiWV16ni/fdm1Cy65xLuVIou5KdiUFOjbN3sr8JUrvceQx6odY8bANdd4v9oYPjz3otMiIhJXHrugP/+cNo2/XHw/X/5vlt9xREIqq3XjnAv/yrtf/IPx7ZK5/fJHyUxQq2tRxNzM9IAB2YV0lj178rhgdeJEuOwyaNkSvv0WKlcOV0QREYlEq1bxt0kfMqlpO75s1dXvNCJhM/HY03giuS/dls7goYkf+B0n6sTczPSqVYU4PmOG1wfXrBmMHQvVq4clm4iIRKgNG+CiizDnePTCu7Sak8Sdj07tQfMta7h95pcsr9GAz9pe4HekqBFzM9ONGx/h+Lx53oWGdepAairUrh22bCIiEoHWrYNzz4XffuO2Pz3Gmqp1/U4k4osnk/7Md8eexlNjX+fMFXP9jhM1Yq6Yfvrp3K3PFSp4x1m8GLp181o60tKgfn1fMoqISIRYvRrOOcdbyWD0aL5v0sbvRCK+yUhI5O5LH2J5jQYM/PpfNN+y2u9IUSHmiunevWHQIGjSxPstXZMm3uPenZZBcrK3xEdqqrfMh4iIxK8VK7xCetMmGDcOunTxO5GI73aVrcCtVz5OemJp3vnin1Tbu8PvSBEv5opp8ArqFSu8FY5WrIDeZ6+GpCTYt88rpI8/3u+IIiLip6VLvSVRt23zflPZqZPfiUQixpqqdbn9igHU27mZN796hjIHD/gdKaLFZDGdw4YN3oz0H394FxuefLLfiURExE8//+zNSO/dC999B6ed5ncikYjzQ4OT+OtF93H66gU8M+ZVcM7vSBEr5lbzyGHLFq+QXrPGK6T1DVNEJL4tWOD9vwAwYQK0auVrHJFINrzlORy7dS33T/2YZTUbMrDTVX5HikixW0xv3+6t2vHrrzByJHTu7HciERHx07x5XiFdujSMHw8nnuh3IpGI91Lna2n2x1oemvgB1ffs4PmzbyC9VGm/Y0WU2Cymd+/21pGeOxe++srrlxYRkfg1Z463mlOlSl4hfdxxficSiQ5m/K37fewoW4m+s76iy4ofueeSB/m1dhO/k0WM2OyZNoOqVeHjj72iWkRE4tf06d6kStWqMGmSCmmRIkovVZrHzu/HzVc+Tq3d2xjxwX3cNHsY5jL9jhYRYrOYrlABhg+Hq9TbIyIS10aN8maka9XyCmktiypSbN8170D3W15hStNTeCJtEO9//gS1d231O5bvYrOYBm0FKyISzxYvhosv9j4aN4aJE6FRI79TiUS9zRWrc+ufHmPA+f3puHohY969i/N/+d7vWL6KzZ5pERGJT5s3wxNPwBtveP3Rzz/P8eubk/7KXGCuv9lEYoUZKe0uYnrj1rw4/HkGffU0n7Q5nyeT/syeMuX9Thd2sTszLSIi8WP/fnj+ea8f+o034I47vNWcHnhAKw+IhMiymo244vrnea3TVVzz0zhGvn8Pp6xb4nessFMxLSIi0cs5+PJLb73oBx/0lkH96Sd49VWoXdvvdCIx70Biaf5zzo30uu5flM44yBeDH+TeKR97K6vFCbV5iIhIRGj68MgijW+9/lf+b/zbnL5mIUtqNeapq//J5Ganwoe/Ab+FJqSI5Glmo5O56OZX+Oe4gdw/9WOoPwKuvRZuu83bNC+Gr2VTMS0iIlGl6da13P39Z/xpwXg2V6jKoxfcyWdtzicjIdHvaCJxbUe5Stx3yYMMbncRXyQuhA8/hDffhLZtvaK6d2+oXt3vmCVOxbSIiES0hMwM2q1bQrelM0j+dQbHbV3D/sRSDDz9Sl4742p2la3gd0QRCTK7YSt49m/w0kvwySfwzjtw993w17/ClVd6hfU558TMbLWKaRERiTgV9++hy4ofSV46k/OWzaLm3h2kJ5RiRqOT+ejUixnT4gx+r1LL75giUpBq1aBfP+/jxx+9onrwYEhJ8S4WvvVWuPFGmr70Q6FfcsWzF4cubzGpmBYRkYhQb8cmkpbOpNvSGXRa9RNlMw6yrVwlxjfvQFrzjkw69lR2lq3od0wRKY527bwLg//zHxg6FN5+Gx55BAYMYEyNhsw/pgXzjzmO+XWPY1HdZuwrXc7vxIWmYlpERPx3+eV8//XXACyvXp8PTr2E1BanM6fBSeqFFokl5ctDnz7exy+/wCefsO7D4ZyzfA5XLkgDIMMS+LVmIxYcc1xUFNgqpkVEYpyZXQi8BCQCbzvnnj3seQs8fxGwB7jJOfdDYc4tMd268cy26qQedzrLazYMyVuISPgUfnWe9nBVe3COY3ZuofWGpbRe/yutNyzNVWAvrdmQtC/qsrFidTZVrM7GSjXYdOi+d7u/dNlDrxyulhAV0yIiMczMEoHXgG7AGmCWmQ1zzi0KGtYdaBH4OB0YCJxeyHNLRv/+DFpVtKXxRCSGmPF7lVr8XqUW41p08o4FCuw2v//Kyb8vpeXG5Ryzayutf19KzT3bSXSZuV5mR5kKbKpUg00Vq0G7XXDNNSGPrmJaRCS2dQSWOueWA5jZp0BPILgg7gl86JxzwHQzq2Zm9YCmhThXRCQ0ggrsscefkeOphMwMau7ZQe3df1Bn11Zq7/4j+2PXH9TZvRUOHAhLzKgopufMmbPZzFaG4KVrAZtD8LqhEk15lTU0oikrRFfeUGVtEoLXLIoGwOqgx2vwZp+PNKZBIc8FwMz6An0DD3eZWaTtKRxNfxcLS59T9IjFz8v3z+mIWzNdf733UXhZn1ORvm9HRTHtnAvJnrBmNts51z4Urx0K0ZRXWUMjmrJCdOWNpqxFlNdCrq6QYwpzrnfQuUHAoKJFC59Y/Prqc4oesfh56XPKFhXFtIiIFNsaoFHQ44bAukKOKVOIc0VE4lqC3wFERCSkZgEtzKyZmZUBegHDDhszDLjBPJ2A7c659YU8V0QkrsX7zHTE/koyH9GUV1lDI5qyQnTljaasheacO2hmdwFj8Ja3e9c5t9DM7gg8/wYwCm9ZvKV4S+PdXNC5PnwaJSEWv776nKJHLH5e+pwCzLt4W0REREREikptHiIiIiIixaRiWkRERESkmOK+mDazJ83sJzOba2Zjzay+35nyY2b/MbOfA3m/MrNqfmcqiJldZWYLzSzTzCJy+Rwzu9DMlpjZUjN72O88+TGzd81so5kt8DvLkZhZIzP7zswWB77+9/qdKT9mVs7MZprZvEDWf/idSUpWtPwbLyozW2Fm8wP/d832O09x5PV9zcxqmNk4M/s1cFvdz4zFkc/n9YSZrQ18veaa2UV+Ziyq/L6vR/PXq4DPqchfq7jvmTazKs65HYH79wAtnXN3+BwrT2Z2PjA+cFHQcwDOuYd8jpUvMzsJyATeBP7qnIuob/iBrZJ/IWirZODakGyVfJTM7GxgF94udSf7nacggZ3z6jnnfjCzysAc4LII/XM1oKJzbpeZlQamAPc656b7HE1KQDT9Gy8qM1sBtHfORe1GIHl9XzOzfwNbnXPPBn74qR7J/8/lJZ/P6wlgl3PueT+zFVd+39eBm4jSr1cBn9PVFPFrFfcz01mFdEBF8tmQIBI458Y65w4GHk7HW/M1YjnnFjvnIm0XtGCHtll2zqUDWVslRxzn3CRgq985CsM5t94590Pg/k5gMd5OehHHeXYFHpYOfETs9wApsqj5Nx6P8vm+1hP4IHD/A7ziJqpE0/frwirg+3rUfr1K8v+quC+mAczsaTNbDfQGHvM7TyHdAnzrd4gol98WylJCzKwp0A6Y4XOUfJlZopnNBTYC45xzEZtViiyW/407YKyZzTFvK/dYUTewxjmB2zo+5ylJdwXaNN+NpnaIwx32fT0mvl55/F9VpK9VXBTTZpZqZgvy+OgJ4Jwb4JxrBKQAd0Vy1sCYAcBBvLy+KkzeCFborZKl6MysEjAUuO+w3wBFFOdchnPuFLzf9HQ0s4huo5EiieV/452dc6cC3YE7A60FErkGAs2BU4D1wH99TVNM0fJ9vSjy+JyK/LWKi01bnHPJhRz6MTASeDyEcQp0pKxmdiPQA0hyEdDwXoQ/20hUmG2WpRgC/cdDgRTn3Jd+5ykM59w2M5sAXAhE/IWeUigx+2/cObcucLvRzL7Ca2mZ5G+qErHBzOo559YHelo3+h2oJDjnNmTdN7O3gBE+ximWfL6vR/XXK6/PqThfq7iYmS6ImbUIengp8LNfWY7EzC4EHgIudc7t8TtPDNBWySEQuKjvHWCxc+5/fucpiJnVtsCqOGZWHkgmgr8HSJHF5L9xM6sYuGAKM6sInE/s/AA4DLgxcP9G4Bsfs5SYQKGZ5XKi7OtVwPf1qP165fc5FedrpdU8zIYCJ+CtOrESuMM5t9bfVHkzs6VAWWBL4ND0SF15BMDMLgdeAWoD24C5zrkLfA11mMCSNy+SvVXy0/4mypuZfQKcC9QCNgCPO+fe8TVUPszsLGAyMB/v3xXAo865Uf6lypuZtcG7aCYRb3JhiHPun/6mkpIULf/Gi8LMjgW+CjwsBXwcjZ9XXt/XgK+BIUBjYBVwlXMuqi7my+fzOhevbcABK4Dbs3qNo0F+39fxeoyj8utVwOd0LUX8WsV9MS0iIiIiUlxx3+YhIiIiIlJcKqZFRERERIpJxbSIiIiISDGpmBYRERERKSYV0yIiIiIixaRiWorEzGqa2dzAx+9mtjZwf5uZLQpzlsvMrGXQ43+aWZE3kTGzpmbm25qfZvboYY+nBW59zSUiIiJHpmJaisQ5t8U5d0pg++U3gBcC908he53GEmNmBe3SeRlwqJh2zj3mnEst6QxhkKOYds6d6VcQERERKRoV01KSEs3sLTNbaGZjAzvKYWbNzWy0mc0xs8lmdmLgeBMzSzOznwK3jQPH3zez/5nZd8BzeZ1vZmfi7Vj5n8DMePPAeVcGXqODmU0zs3lmNtPMKgdmeieb2Q+BjwKLVvO8amaLzGykmY0Kev0VZlYrcL99YBtqzKxj4H1/DNyeEDh+k5l9Gfg8fjWzfweOPwuUD3wOKYFju/LIkmhm/zGzWYE/r9sDx+uZ2aTA+QvMrMtRfg1FRESkCAqa9RMpqhbAtc65P5vZEOBPwGBgEN7Okr+a2enA60BX4FXgQ+fcB2Z2C/Ay3mwzwPFAsnMuw8zSDj/fOdfVzIYBI5xzXwB4O4NCYNvgz4BrnHOzzKwKsBfYCHRzzu0zbxv5T4D2BXw+l+PtjtkaqAssAt49wp/Bz8DZzrmDgZaTZwJ/DuDN3rcD9gNLzOwV59zDZnZXYHa/ILcC251zHcysLDDVzMYCVwBjnHNPm1kiUOEIryMiIiIlSMW0lKTfnHNzA/fnAE3NrBJwJvB5VrGLtyU6wBl4xSDAR8C/g17r80AhXdD5+TkBWO+cmwXgnNsBYGYVgVfN7BQgA69gL8jZwCfOuQxgnZmNP8J4gKrAB4Fi3QGlg55Lc85tD2RZBDQBVhfiNQHOB9pkzYwH3qcFMAt418xKA18H/fmLiIhIGKiYlpK0P+h+BlAer5VoWyFmXsErPrPsDtwW5fwsdthrZbkf2AC0DbzuviJmCnaQ7DapckHHnwS+c85dbmZNgQlBzx3+51OUf38G3O2cG5PrCbOzgYuBj8zsP865D4vwuiIiInIU1DMtIRWYFf7NzK6CQ33IbQNPTwN6Be73BqYU8fydQOU83vZnoL6ZdQicUzlwIWNVvBnrTOB6IPEI8ScBvQL9yvWA84KeWwGcFrj/p6DjVYG1gfs3HeH1sxwIzCwXZAzQL2ucmR1vZhXNrAmw0Tn3FvAOcGoh31NERERKgIppCYfewK1mNg9YCPQMHL8HuNnMfsIrbu8t4vmfAg8GLvZrnjXYOZcOXAO8EjhnHN7s8evAjWY2Ha/FYzcF+wr4FZgPDAQmBj33D+AlM5uMN8uc5d/Av8xsKkcu1rMMAn7KugAxH2/j9Wz/YN5yeW/izWyfC8w1sx/xivqXCvmeIiIiUgLMufx+iy0iwczsfYIueBQRERHRzLSIiIiISDFpZlpEREREpJg0My0iIiIiUkwqpkVEREREiknFtIiIiIhIMamYFhEREREpJhXTIiIiIiLF9P/gbI9ttYQzIgAAAABJRU5ErkJggg==\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "import numpy as np \n", - "import scipy.stats as stats\n", - "import matplotlib.pyplot as plt\n", - "\n", - "plt.rcParams['figure.figsize'] = [12, 6]\n", - "\n", - "mu, sigma = 10, 4\n", - "n = 1000 # с ростом числа точек в распределении qq-plot стремится к прямой\n", - "sequence = np.random.normal(mu, sigma, n)\n", - "\n", - "\n", - "fig, (ax1, ax2) = plt.subplots(1, 2)\n", - "fig.suptitle('QQ Plot', fontsize=18)\n", - "\n", - "# Q-Q Plot graph\n", - "stats.probplot(sequence, dist=\"norm\", plot=ax1)\n", - "ax1.set_title(\"Normal Q-Q Plot\")\n", - "\n", - "# normal distribution histogram + distribution\n", - "count, bins, _ = ax2.hist(sequence, 25, density=True)\n", - "p_x = 1/(sigma * np.sqrt(2 * np.pi)) * np.exp( - (bins - mu)**2 / (2 * sigma**2) )\n", - "ax2.plot(bins, p_x, color='r')\n", - " \n", - "\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Однофакторный дисперсионный анализ\n", - "\n", - "Рассмотренный ранее **t-критерий Стьюдента** (равно как и его непараметрические аналоги) предназначен для сравнения исключительно **двух совокупностей**. В таком случае мы можем применять однофакторный дисперсионный анализ. Та переменная, которая будет разделять наших испытуемых или наблюдения на группы (номинативная переменная с нескольким градациями) называется **независимой переменной**. А та количественная переменная, по степени выраженности которой мы сравниваем группы, называется **зависимая переменная**. \n", - "\n", - "\n", - "$$ SS_{total} = \\sum_{j=1}^{p}{\\sum_{i=1}^{n_j}{(x_{ij} - \\bar{x})^2}} = SS_{between} + SS_{within} $$\n", - "$$ SS_{between} = \\sum_{j=1}^{p}{n_j{(\\bar{x}_j - \\bar{x})^2}} $$\n", - "$$ SS_{within} = \\sum_{j=1}^{p}{\\sum_{i=1}^{n_j}{(x_{ij} - \\bar{x}_j)^2}} $$\n" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Нулевая гипотеза: a=b=c\n", - "Альтернативная гипотеза: !(a=b=c)\n", - "Результат:\n", - "отклоняем нулевую гипотезу\n" - ] - }, - { - "data": { - "image/png": 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "from scipy import stats\n", - "import pandas as pd\n", - "\n", - "# Выборки которые надо сравнить\n", - "data = pd.DataFrame({\n", - " 'a': [3, 1, 2],\n", - " 'b': [5, 3, 4],\n", - " 'c': [7, 6, 5]\n", - " })\n", - "data.boxplot()\n", - "print('Нулевая гипотеза:', '='.join(data))\n", - "print('Альтернативная гипотеза:', f'!({\"=\".join(data)})')\n", - "# общая средняя\n", - "grand_mean = data.values.flatten().mean()\n", - "# отклонение групповых средний от общей средней\n", - "ssb = sum(data[group].size * (group_mean - grand_mean)**2 for group, group_mean in data.mean().items())\n", - "# отклонения значений в внутри группы от средней группы\n", - "ssw = sum(sum((x - group_mean)**2 for x in data[group]) for group, group_mean in data.mean().items())\n", - "\n", - "groups = data.shape[1]\n", - "dfb = groups - 1\n", - "dfw = data.size - groups\n", - "# межгрупповой средний квадрат \n", - "mssb = ssb/dfb\n", - "# внутригрупповой средний квадрат\n", - "mssw = ssw/dfw\n", - "\n", - "f_value = mssb/mssw\n", - "\n", - "p = stats.f.sf(f_value, dfb, dfw)\n", - "print('Результат:')\n", - "if p < 0.05:\n", - " print('отклоняем нулевую гипотезу')\n", - "else:\n", - " print('НЕ отклоняем нулевую гипотезу')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Множественные сравнения в ANOVA\n", - "\n", - "В отличие от t-критерия, позволяет сравнивать средние значения трёх и более групп. Разработан Р. Фишером для анализа результатов экспериментальных исследований. В литературе также встречается обозначение **ANOVA** (от англ. **AN**alysis **O**f **VA**riance) - дисперсионный анализ\n", - "\n", - "## почему мы не можем применить t-критерий для более двух выборок\n", - "**применяя его попарно к каждой выбрке**\n", - "\n", - "Чтобы выяснить это, сделаем эксперемент." - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "from numpy import random\n", - "import matplotlib.pyplot as plt\n", - "from scipy.stats import t\n", - "\n", - "\n", - "def pair_t(samples, alpha):\n", - " '''Парный t-критерий, если все выборки равны, возвращает True'''\n", - " n_samples = samples.shape[0]\n", - " # https://ru.wikipedia.org/wiki/Сочетание \n", - " n_combinations = n_samples*(n_samples - 1)//2\n", - " result = np.zeros(n_combinations, dtype=bool)\n", - " k = 0\n", - " for i in range(n_samples):\n", - " for j in range(i+1, n_samples):\n", - " N = samples[i].size\n", - " std_err = np.sqrt((samples[i].std()**2)/N + (samples[j].std()**2)/N)\n", - " t_value = (samples[i].mean() + samples[j].mean())/std_err\n", - " p = t.sf(t_value, N-2)\n", - " result[k] = p >= alpha\n", - " k += 1\n", - " return np.all(result)" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": {}, - "outputs": [], - "source": [ - "def pair_t_test(repeat, n_samples, sample_size, ax, alpha=0.05):\n", - " '''\n", - " функция показывает, сколько у нас будет ложных результатов, при парном сравнение множества выборок\n", - " с помощью t-критерия\n", - " \n", - " repeat, n_samples, sample_size = количество повторов, количество выборок в каждом повторе, размер выборки\n", - " \n", - " ax - для рисования\n", - " alpha = (1 - (p-уровень значимости))\n", - " '''\n", - " result = np.zeros(repeat, dtype=bool)\n", - " for i in range(repeat):\n", - " samples = random.randn(n_samples, sample_size)\n", - " result[i] = pair_t(samples, alpha)\n", - " \n", - " unique, counts = np.unique(result, return_counts=True)\n", - " percentage = counts/result.size\n", - " ax.pie(percentage, normalize=False, labels=unique, autopct='%.0f%%')" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, axs = plt.subplots(ncols=4, figsize=(20, 4))\n", - "n_samples = [2, 4, 8, 16]\n", - "fig.suptitle('Процент ошибок при попарном сравнение выборок t-критерием')\n", - "\n", - "for n, ax in zip(n_samples, axs):\n", - " pair_t_test(1000, n, 100, ax)\n", - " ax.set_title(f'{n} samples')\n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Как мы и ожидаем, степень ошибки равна **5%**, при сравнение **двух выборок** из одной ГС с помощью t-критерия с p-уровнем значимости **95%**. Если мы возмём **4** выборки, и сравним их попарно, то ошибка возрастёт в **4** раза до **20%**. При **8** выборок, наша ошибка возрасла почти в **9** раз до **46%**. **16** выборок дают увеличение ошибки до **80%** ( в 16 раз), что совершенно неприемлемо." - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, axs = plt.subplots(ncols=4, figsize=(20, 4))\n", - "n_samples = [2, 4, 8, 16]\n", - "fig.suptitle('Процент ошибок при попарном сравнение выборок t-критерием с корректировкой уровня значимости')\n", - "\n", - "for n, ax in zip(n_samples, axs):\n", - " alpha = 0.05/((n*(n-1))/2)\n", - " pair_t_test(1000, n, 100, ax, alpha)\n", - " ax.set_title(f'{n} samples')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Однако в данном случае эта будет арх-консервативная корректировавка, которая имеет меньше вероятность найти реальные значения. По сути мы **уменьшаем шанс получить ошибку I рода, но увеличиваем шанс на ошибку II рода**.\n", - "\n", - "### Ошибки первого и второго рода\n", - "\n", - "" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Многофакторный ANOVA\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "
" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Часть 3" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Корреляция\n", - "\n", - "### Ковариация \n", - "\n", - "(ко - совместная, вариация - изменчивость). Мера **линейной** зависимости двух случайных величин.\n", - "\n", - "Если ковариация положительна, то с ростом значений одной случайной величины, значения второй имеют тенденцию возрастать, а если знак отрицательный — то убывать.\n", - "\n", - "$$ cov(X, Y) = \\frac{\\sum{(x_i - \\bar{x})(y_i - \\bar{x})}}{N - 1} $$\n", - "где N - количество случайных величин, а единица - количество степеней свободы.\n", - "\n", - "Однако только по **абсолютному** значению ковариации **нельзя судить** о том, **насколько сильно величины взаимосвязаны**, так как масштаб ковариации зависит от их дисперсий. Значение ковариации можно нормировать, поделив её на произведение среднеквадратических отклонений (квадратных корней из дисперсий) случайных величин. Полученная величина называется коэффициентом корреляции Пирсона, который всегда находится в интервале от −1 до 1:" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "$$ r(x, y) = \\frac{cov(x, y)}{\\sigma_x\\sigma_y}$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Подробнее про формулу корреляции\n", - "\n", - "Давайте остановимся на формуле коэффициента корреляции, которую мы получили:\n", - "$$ r(x, y) = \\frac{cov(x, y)}{\\sigma_x\\sigma_y}$$\n", - "запишем формулу чуть подробнее и выполним возможные преобразования:\n", - "\n", - "$$ r(x, y) = \\frac{\\sum{(x_i - \\bar{x})(y_i - \\bar{y})}}{(N - 1)\\sqrt{\\sum{\\frac{(x_i - \\bar{x})^2}{N-1}}}\\sqrt{\\sum{\\frac{(y_i - \\bar{y})^2}{N-1}}}} $$\n", - "\n", - "теперь вынесем 1/ (N - 1) из под корней \n", - "\n", - "$$ r(x, y) = \\frac{\\sum{(x_i - \\bar{x})(y_i - \\bar{y})}}{(N - 1)\\frac{1}{(N-1)}\\sqrt{\\sum{(x_i - \\bar{x})^2}}\\sqrt{\\sum{(y_i - \\bar{y})^2}}} $$\n", - "\n", - "и сократим (N - 1)\n", - "\n", - "$$ r(x, y) = \\frac{\\sum{(x_i - \\bar{x})(y_i - \\bar{y})}}{\\sqrt{\\sum{(x_i - \\bar{x})^2}}\\sqrt{\\sum{(y_i - \\bar{y})^2}}} $$\n", - "\n", - "таким образом, мы сократили N - 1 в знаменателе и получили финальную формулу для коэффициента корреляции, которую вы часто сможете встретить в учебниках:\n", - "\n", - "$$ r(x, y) = \\frac{\\sum{(x_i - \\bar{x})(y_i - \\bar{y})}}{\\sqrt{\\sum{(x_i - \\bar{x})^2}\\sum{(y_i - \\bar{y})^2}}} $$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Примеры 3.1" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": {}, - "outputs": [], - "source": [ - "'''Демонстрация работы ковариации и корреляции'''\n", - "import numpy as np\n", - "import random as r\n", - "\n", - "def cov(x, y):\n", - " assert x.size == y.size\n", - " return ((x - x.mean()) * (y - y.mean())).sum()/(x.size - 1)\n", - "\n", - "def cor(x, y):\n", - " return cov(x, y)/(np.std(x, ddof=1)*np.std(y, ddof=1))\n", - "\n", - "# функция имитирущая случаные факторы\n", - "# р - настолько существенным будет случайный фактор\n", - "def randomize(arr, p):\n", - " alpha = np.max(arr) - np.min(arr)\n", - " res = np.zeros(arr.shape)\n", - " for i, v in enumerate(arr):\n", - " sign = 1 if r.choice([True, False]) else -1\n", - " res[i] = v + sign*alpha*r.random()*p\n", - " return res" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": {}, - "outputs": [], - "source": [ - "x = np.array(range(30))\n", - "y = randomize(x, 0.1)\n", - "y1 = randomize(x, 0.5)\n", - "y2 = randomize(x, 1)" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt\n", - "\n", - "fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(16, 3))\n", - "ax1.scatter(x, y)\n", - "ax2.scatter(x, y1)\n", - "ax3.scatter(x, y2)\n", - "ax1.set_title('высокая корреляция')\n", - "ax2.set_title('средняя корреляция')\n", - "ax3.set_title('низкая корреляция')\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "cov1: 75.61\n", - "cov2: 77.81\n", - "cov3: 86.23\n", - "\n", - "cor1: 0.98\n", - "cor2: 0.75\n", - "cor3: 0.51\n", - "\n" - ] - } - ], - "source": [ - "print(f'''\n", - "cov1: {cov(x, y):.2f}\n", - "cov2: {cov(x, y1):.2f}\n", - "cov3: {cov(x, y2):.2f}\n", - "\n", - "cor1: {cor(x, y):.2f}\n", - "cor2: {cor(x, y1):.2f}\n", - "cor3: {cor(x, y2):.2f}\n", - "''')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Регрессия с одной независимой переменной\n", - "\n", - "В этой и следующих главах мы научимся работать с **одномерным регрессионным анализом**, который позволяет проверять гипотезы о взаимосвязи одной количественной зависимой переменной и нескольких независимых.\n", - "\n", - "Сначала мы познакомимся с самым простым вариантом - простой **линейной регрессией**, при помощи которой можно исследовать взаимосвязь двух переменных. Затем перейдем к множественной регрессии с несколькими независимыми переменными.\n", - "\n", - "Линейная регрессия (англ. Linear regression) — используемая в статистике регрессионная модель зависимости одной (объясняемой, зависимой) переменной $y$ от другой или нескольких других переменных (факторов, регрессоров, независимых переменных) $x$ с **линейной функцией зависимости**.\n", - "\n", - "В общем виде функция линейной регрессии выглядит как:\n", - "\n", - "$$ y = b_0 + b_1x $$\n", - "$b_0$ - intercept значение пересечения линии с осью Y \n", - "\n", - "$b_1$ - slope задаёт наклон линии регрессии\n", - "\n", - "строят регрессионную прямую методом наименьших квадратов (МНК)\n", - "\n", - "МНК - это способ нахождения оптимальных параметров линейной регресссии ($b_0$, $b_1$), таких, что сумма квадратов ошибок (остатков) была минимальная.\n", - "\n", - "Расчёт параметров идёт по таким формулам:\n", - "\n", - "$$ b_1 = \\frac{sd_y}{sd_x}r_{xy} $$\n", - "$$ b_0 = \\bar{Y} - b_1\\bar{X} $$" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "'''Демонстрация МНК'''\n", - "b1 = y1.std()/x.std()*cor(x, y1)\n", - "b0 = y1.mean() - b1*x.mean()\n", - "f = lambda x: b0 + b1*x\n", - "y_pred = f(x)\n", - "plt.scatter(x, y1)\n", - "plt.plot(x, y_pred, color='r')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Гипотеза о значимости взаимосвязи и коэффициент детерминации\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Условия применения линейной регрессии с одним предиктором" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Применение регрессионного анализа и интерпретация результатов" - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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statemetro_reswhitehs_gradpovertyfemale_house
0Alabama55.471.379.914.614.2
1Alaska65.670.890.68.310.8
2Arizona88.287.783.813.311.1
3Arkansas52.581.080.918.012.1
4California94.477.581.112.812.6
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" - ], - "text/plain": [ - " state metro_res white hs_grad poverty female_house\n", - "0 Alabama 55.4 71.3 79.9 14.6 14.2\n", - "1 Alaska 65.6 70.8 90.6 8.3 10.8\n", - "2 Arizona 88.2 87.7 83.8 13.3 11.1\n", - "3 Arkansas 52.5 81.0 80.9 18.0 12.1\n", - "4 California 94.4 77.5 81.1 12.8 12.6" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "''''''\n", - "import pandas as pd\n", - "import seaborn as sns\n", - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "\n", - "df = pd.read_csv('data/states.csv')\n", - "df.head()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Есть данные по штатам с различными значениями:\n", - " - **metro_res** - процент населения живущие в столице\n", - " - **white** - процент белого населения\n", - " - **hs_grad** - процент людей со образованием\n", - " - **poverty** - уровень бедности\n", - " - **female_house** - процент домов, где есть домохозяйки \n", - " \n", - "Исследуем связь уровня образования и бедности, где бедность будет ЗП, а уровень образования НП.\n", - "\n", - "Первое, что нам необходимо сделать, это построить линейную модель, которая наилучшим образом будет описывать наши данные.\n", - "\n", - "$$ \\hat{y} = b_0 + b_1x $$\n", - "\n", - "Далле, построив нашу модель, нам надо узнать, насколько хорошо наша объясняет ЗП, для этого найдём коэфицент детерминации $R^2$\n", - "\n", - "Проверим нулевую гипотезу:\n", - "$$ b_1 = 0 : H0$$\n", - "\n", - "Третья наша задача, это задача предсказания, по данным НП мы хотим предсказать ЗП." - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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countmeanstdmin25%50%75%max
metro_res51.072.24902015.27589438.260.8071.686.80100.0
white51.081.71960813.89722325.976.8085.490.2597.1
hs_grad51.086.0117653.72599877.283.3086.988.7092.1
poverty51.011.3490203.0991855.69.2510.613.4018.0
female_house51.011.6333332.3561557.89.5511.812.6518.9
\n", - "
" - ], - "text/plain": [ - " count mean std min 25% 50% 75% max\n", - "metro_res 51.0 72.249020 15.275894 38.2 60.80 71.6 86.80 100.0\n", - "white 51.0 81.719608 13.897223 25.9 76.80 85.4 90.25 97.1\n", - "hs_grad 51.0 86.011765 3.725998 77.2 83.30 86.9 88.70 92.1\n", - "poverty 51.0 11.349020 3.099185 5.6 9.25 10.6 13.40 18.0\n", - "female_house 51.0 11.633333 2.356155 7.8 9.55 11.8 12.65 18.9" - ] - }, - "execution_count": 32, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "df_descr = df.describe().transpose()\n", - "df_descr" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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iJZwtS83sH9suueQSHn/8cebPn8/tt9/O77//Xuxry7tfNFLSHE0OPNCXaqxaBddf7ycNNmkC557r66Al5nVtWZdZ/duzKutUZvVvr4RZRETCIlwlgW3btuWtt96ioKCAjRs38s477wCwceNG9t9/fwoLCxk1atSf++++++5s3Ljxz8cl7RcLlDRHo/33h/vvh9xc32Fj0iRo3hy6dvUdOERERERKEa6SwMMPP5xzzz2XFi1acOaZZ9KmTRsABg8ezNFHH02HDh045JBD/tz/vPPOY9iwYbRs2ZIVK1aUuF8sUPeMWLBhg1+BfvhhyM+HTp3g1lvh2GODjkxEREQiJFq6Z8STinTPCNsYbalEe+3lB6L85z/wxBPw4IPQujW0b++T53bt/CRCERERkZCuLesqSa5EKs+IJXvsAQMG+LKNBx6ARYv8sJS2bWHyZIiB3xoEpaLjq0VERESKUtIci3bdFW64AVau9GUbubm+ZOPoo2H8eCXP2wlXr0oRERFJHEqaY1lKCvz7376n8/Dh8P33cPrp0LIlvPEGbN0adIRRIVy9KkVERCItFu5FixUV/V4qaY4Hu+wCV1wBS5f6YSkFBX7SYNOmMGoUbN4cdISBCmevShERkUipXr06P/zwgxLnSuCc44cffqB69erlfo1uBIwnyclw8cVw4YV+pXnIEP/5HXf4WuiLLvL7JJg6qSnkFZMga3y1VAbdnS4ikVKvXj3WrFnD+vXrgw4lLlSvXp169eqVe3+1nItnW7dCdrZPnnNyoH593/e5Z0+oVi3o6CJmW01z0RKNlOQkTeOTnaafLRGR+FNSyzmVZ8SzKlWgWzc/EGXCBNhvP+jTx4/tfuQR+O23oCOMCI2vlnBRvbyISOLQSnMicQ4++AAGD4YZM2CffaBvX59I77Zb0NGJxJz0/hMp7m9QA1ZlnRrpcEREpBJopVn8AJR//Qs++sh/HHYY3HSTL9sYMgR++inoCEViSkl18aqXFxGJP0qaE1XbtjBlCnz6qR/HfeutPnm+7Tb44YegoxOJCf06ZpCSnPS3bSnJSfTrmBFQRCIiEi5KmhPdMcfAO+/A3Llw4om+dCMtDW6+Gb77LujoRKKa6uVFRBKHaprl7xYuhLvvhjFjfIeNK6/0dc91lQSIiIhI/FNNs5TPoYfCq6/C4sVw7rl+THeDBnDVVbB6ddDRiYiIiARCSbMU7+CDYcQIWLYMLrkEnnsOGjWCyy6D5cuDjk5EREQkopQ0S+nS0+GZZ2DlSt+a7tVXISPDTxdcvDjo6EREREQiQkmzlE+9evDoo7BqFdxwA4wb50s5zjkHvvwy6OhEREREwkpJs1TMfvvBsGG+vnnAAHjvPWjRAk4/HXSzpoiIiMQpJc2yY2rV8l02Vq+GO++Ejz+GI4+Ek0+GWbOCjk5ERESkUilplp2z555+IEpuLmRlwZw5cNxx0L49TJvmR3eLiIiIxLiwJc1m9oKZfWdmC7bbfo2ZLTWzhWZ2X7jOLxG2xx5+IMqqVfDgg7BkiR+WctxxvoSjmOQ5OyeP1lnTSO8/kdZZ08jOyQsgcBEREZGyhXOleSTQqegGMzsBOB1o7pw7FLg/jOeXIOy6K/znP77bxuOPwzff+JKNo46Ct9/+M3nOzsljwLj55OUX4IC8/AIGjJuvxFlERESiUtiSZufcDGDDdpv7AFnOuT9C+2hOc7yqXh2uvtr3dH72WdiwAbp29TcNvvEG909aTEHhlr+9pKBwC8MmLw0kXBEREZHSRLqm+WCgjZl9bmYfmdmRJe1oZr3MbLaZzV6/fn0EQ5RKtcsucPnlsHQpvPgi/PEHnHMOIx68lK4Lp5O09e+J89r8goACFRERESlZpJPmqsCewDFAP+B1M7PidnTODXfOZTrnMmvXrh3JGCUcqlaFHj1g4UJ47TWqVK3KwxMe4INne3P2V1NI3lIIQJ3UlIADFREREfmnSCfNa4Bxzvs/YCtQK8IxSJCSkuDcc5k/8SOuOWsQG6vVYNikR5k+vBc9v5rEzcfXDzpCERERkX+IdNKcDbQHMLODgV2A7yMcg0SBrkccwIm39Kb3dc/Q86zbya9Zi9snPUGXM9vCww/Db78FHaKIiIjIn8yFqY+umY0GjsevJH8L3A68DLwAtAA2AX2dc9PKOlZmZqabrWlz8c0539d58GD46CPYZx+48Ubo0wd23z3o6ERERCRBmNkc51zmP7aHK2muTEqaE8zHH/vkeepU2GsvuP56uOYaSE0NOjIRERGJcyUlzZoIKNGnTRuYMgU++wyOPdZPHKxfHwYNgh9+CDo6ERERSUBKmiV6HX00vPMOzJ0L//oX3H23T55vugm+/Tbo6ERERCSBKGmW6NeyJbz5JixYAF26wAMPQHq6L9vI0wRBERERCT8lzRI7Dj0UXn0VFi+Gc8/1Y7obNPA3C65eHXR0IiIiEseUNEvsOfhgGDECli2DSy6B55+HRo3gssv82G4RERGRSqakOYFk5+TROmsa6f0n0jprGtk5MV7akJ4OzzwDK1f61eZXX4WMDLjwQr8aLSIiIlJJlDQniOycPAaMm09efgEOyMsvYMC4+bGfOAPUqwePPgqrVsENN8Bbb/lSjrPPhi+/DDo6ERERiQNKmhPEsMlLKSjc8rdtBYVbGDZ5aUARhcF++8GwYb6+ecAAmDwZWrSA00+HL74IOjoRERGJYUqaE8Ta/IIKbY9ptWr59nSrV8Odd/phKUcdBZ06waxZQUcnIiIiMUhJc4Kok5pSoe1xYc89/WCU3FwYOhTmzIHjjoP27f3I7hiYhikiIiLRQUlzgujXMYOU5KS/bUtJTqJfx4yAIoqgPfaA/v198vzgg7BkCZx4ok+g33tPybOIiIiUSUlzgujasi5DuzWjbmoKBtRNTWFot2Z0bVk36NAiZ9dd4T//8d02nngCvvkGTj7Zl268/baSZxERESmRuRhIFDIzM93s2bODDkPizaZN8PLLcM89PpFu3hwGDoQzz4SkpLJfLyIiInHHzOY45zK3366VZklcu+ziB6IsXQovvQR//OEnDTZtCq+8Aps3Bx2hiIiIRAklzSJVq8JFF8HChTBmDCQn+8eHHOKnDW7aFHSEIiIiEjAlzSLbJCXBOefAvHl+QEpqKlx+ORx0EDz1FPz+e9ARioiISECUNItsr0oV6NrVD0R5912oWxeuugoaNoSHH4bffgs6QomwuBtBLyIiFaakWaQkZr67xqxZ8MEHcPDBvvtGejrcdx9s3Bh0hBIBcT2CXkREyk1JsyScCq8amvmBKNOn++mCLVvCzTdDWhoMHgz5+ZEIWwKSECPoRUSkTEqaJaHs9KrhtoEon38OrVv7iYP168OgQfD992GNXYKRUCPoRUSkREqaJaFU2qrhUUfB+PGQkwMnneR7PaelwU03wbffVl7AEriEHEEvIiL/oKRZEkqlrxq2aAFvvAELFsDpp8MDD/jk+brrIE81r/EgoUfQi4jIn5Q0S0IJ26phkyYwahQsWQLnnw9PPgkNGkDv3pCbu3PHlkBpBL2IiIDGaEuC2VbTXLREIyU5qfKToNxcyMqCESNg61Y/LGXAAN/zWURERKKWxmiLEMFVw7Q0ePppWLHC93gePdpPGOzeHRYtqtxziYiISNhppVkkEr791tc7P/mkH45y5pkwcKCviRYREZGooZVmkQj7Wz/oEQvJPv86X7Zxyy0wZYrv99yli588KCIiIlFNSbNIGJTYD/qbP2DIEFi9Gu66y08bPOoo6NQJZs4MOmwREREpgZJmkTAosx90airceqtfeb73Xt/vuU0bOOEEmDYNYqBsSkREJJGELWk2sxfM7DszW1DMc33NzJlZrXCdXyRI5e4HvfvufiDKqlXw8MPw9ddw4ol+2uCkSUqeRUREokQ4V5pHAp2232hmBwAdgP+G8dwigapwP+gaNfxAlBUr/M2CeXlwyilw5JGQne3b1iWIv9WCZ00r/4hzERGRMApb0uycmwFsKOaph4CbAC2hSdza4Sly1atDnz6wbBk8/zzk58MZZ/guG6+/Dlu2lP76GFdiLbgSZxERCVhEa5rNrAuQ55z7MpLnFYm0ne4HvcsucOmlfsLgyy9DYSGcey40beofb94c1viDUmYtuIiISEDC2qfZzNKACc65pmZWA5gOnOSc+8nMcoFM59z3Jby2F9AL4MADDzxi9erVYYtTJOpt2QLjxvnOG1995Ud0DxgAPXr4BDtOpPefWOyvoAxYlXVqpMMREZEEFA19mhsC6cCXoYS5HjDXzPYrbmfn3HDnXKZzLrN27doRDFMkCiUlwdln+y4bb78Ne+0FV1zhx3I/+ST8/nvQEVaKCteCi4iIREjEkmbn3Hzn3D7OuTTnXBqwBjjcOfe/SMUgEvOqVPEDUf7v/3x3jXr14Oqr/crzQw/5aYMxbIdrwUVCdCOpiIRLOFvOjQY+BTLMbI2ZXRauc4kkHLO/BqJMmwaHHAI33ABpaZCVBRs3Bh3hDtnpWnBJaLqRVETCKaw1zZUlMzPTzZ49O+gwRKLbrFkweDBMngx77gnXXw/XXusHqYgkgNZZ08grpkd63dQUZvVvH0BEIhKLoqGmWUTCqXVreO89X7rRpg3cfjvUrw8DB8L3xd5vKxJXyj1USERkByhpFqkkUVNLeeSR/mbBefOgY0cYOtQnz337wv90C4HEL91IKiLhpKRZpBJEZS3lYYf5gSgLFkC3bv5GwfR0X7KxZk1wcYmEiW4kFZFwUtIsUgmieihHkyZ+IMrSpXDBBfDUU77bxpVXwqpVQUcnUml0I6mIhJNuBBSpBDE1lCM3F+67z4/p3rIFLrrID0o5+OCgIxMREQmcbgQUCaOYqqVMS/MDUVauhGuugTFjoHFjvwq9cGFYTx01dd8iIiIVpKRZpBLEZC1l3bq+znnVKn+T4Pjx0LQpnHmmnzxYyaKy7ltERKSclDSLVIKYrqXcd1+4915YvRoGDYL334fDD4fTToPPP6+000R13beIiEgZVNMsIn+Xnw+PP+5XoTdsgA4d4NZbfe/nnRBTdd8iIpKwVNMsEqWipc73zziyZtG66rFMePsTvwL95ZfQti20a+dXoXfwP9oxVfctIiKyHSXNIgGKljrf4uLoN3kV2R26+5rnhx+G5cv9qvOxx8LEiRVOnmOy7ltERCRESbNIgKKlzrfUOGrUgOuugxUrfNeNtWuhc2fIzIS33oKtW8t1jpiu+xYRkYRXNegARBLZ2vyCCm0PNI7q1aFPH7jsMnjlFbjnHj9psGlTGDgQzj4bkpKKPc42XVvWVZIsIiIxSSvNIgGKljrfCsWxyy5w6aWwZImfNLh5M5x/vp88+OKL/rGIiEicUdIsEgEl3ewXLXW+OxRH1apw4YWwYAG8/rpfib7kEj9Z8NlnYdOm8AYtIiISQUqaRcKstJv9oqXOd6fiSErypRk5OfD227D33tCrFzRs6FvX/f572OMXEREJN/VpFgmz1lnTyCumZrhuagqz+rcPIKIwcw4mT4bBg+GTT2C//aBfP7jySth116CjExERKZX6NIsEJFpu9osYM+jUCWbOhGnToHFjuPFGSEuDoUPh55+DjlBERKTClDSLhFm03OwXcWZwwgk+cZ4507eou+UWnzzfeSf8+GPQEYqIiJSbkmaRMIuWm/0C1bo1TJoE//d/frrgHXdA/fo+if7++6CjExERKZOSZpEwi5ab/aLCkUdCdjbMm+dLOLKyfPLcty/8739BRyciIlIi3QgoIsFZvNgPSXn1VUhOhiuugJtuggMOCDoyERFJULoRUESiT+PGfkDK0qXQvTs8/bRvVXfllbBqVdDRiYiI/ElJs4gEr1EjeP55WL4cLr8cRo6Egw6Cnj3h66+Djk5ERERJs4hEkfr14cknYeVKuOYaGDPGr0ZfcIGfPCgiIhIQJc0iEn3q1oWHHvIlGn37wjvvQLNmcOaZfvKgiIhIhClpFpHote++cO+9kJsLt94KH3wAhx8OnTvD558HHZ2IiCQQJc0iEv323hvuugtWr4YhQ+DTT+GYY6BDB5gxI+joREQkAajlnIjEnl9+gaeegvvvh+++4/vDj2ZwyzMZv3dj6uxZg34dM/7RBzs7J49hk5eyNr+AOqkpxe4jIiIS8ZZzZvaCmX1nZguKbBtmZkvM7Csze8vMUsN1fhGJY7vtBv36QW4uX/W7k83LlvPI8zcx7uW+HDxnBgPe/IrsnLw/d8/OyWPAuPnk5RfggLz8AgaMm/+3fUREREoTzvKMkUCn7bZNBZo655oDXwMDwnh+EYl3KSn02es42vZ6jls6Xk3tX39kxNg7eeO5a/i/B56DrVsBGDZ5KQWFW/720oLCLQybvDSIqEVEJAaFLWl2zs0ANmy3bYpzbnPo4WdAvXCdX0QSw9r8AjZVTebVFidzfK/h9D3lempsKuCeUXfAYYfBa6/xvw2/lPhaERGR8qga4LkvBcYEeH4RiQN1UlPICyW/m5OqMrbZv3jr0BO46L+fc8f8bDj/fKbXqscjR53N203asTmp6t9eK7FBNekiErRAumeY2UBgMzCqlH16mdlsM5u9fv36yAUnIjGlX8cMUpKT/rZtl2q70OLmq2D+fBg7lpp77cED7z7EtGev5Lx575G8pZCU5CT6dcwIKGqpCNWki0g0iHjSbGYXA52B7q6U1h3OueHOuUznXGbt2rUjF6CIxJSuLesytFsz6qamYEDd1BSGdmvmVyGrVIEzz6TmkgV89tAIftk9lazJjzPz2V68tmk2XQ/ZK+jwo1Z2Th6ts6aR3n8irbOmBZqgqiZdRKJBWFvOmVkaMME51zT0uBPwINDOOVfu5WO1nBORSuEcTJ0KgwfDzJmw335+4mDv3rDrrkFHFzW2rewWTVRTkpP++s9IhKX3n0hx/1IZsCrr1EiHIyJxLoiWc6OBT4EMM1tjZpcBjwO7A1PNbJ6ZPR2u84uI/IMZnHSSH4gyfToceqhPmtPSYOhQ+PnnoCOMCtG2sltS7blq0kUkksLZPeN859z+zrlk51w959zzzrlGzrkDnHMtQh+9w3V+EZESmcHxx8P778Mnn8CRR8Itt0D9+nDHHfDjj0FHGKiSuooE1W2kuLp11aSLSKRpjLaIJLZWreDdd2H2bJ9I33mnT55vuQUS9CbkaFvZLbVuXUQkQipU02xm1YFdnHMR/R2mappFJGK++gruvhveeANSUny9c9++sP/+QUcWMdFW0ywiEkk7XdNsZpcDk4GJZnZPZQYnIhI1mjeHMWNg0SI480x45BFIT4drroFvvgk6uojQyq6IyD+VuNJsZqc5594p8vg159x5oc+/dM4dFqEYtdIsIsFZsQKysmDkSF8Lfckl0L8/NGgQdGQiIhIGO7LSfJiZvW1m25Ljr8xslJm9AiwMS5QiItGmYUN49lmfPF9xBbz0Ehx8MFx8MSxVn2ARkURRak2zme0H3BV6eBuwG1DDOfdVBGL7k1aaRSRqrF0L998PTz8Nv/8O554LAwdC06YVPpRGQ4uIRJ8drWn+FbgeeAIYDpwPfF3p0YmIxIo6deDBByE3F266CSZMgGbNoFs3mDu33IfRaGgRkdhSYtJsZkOAicAHwAnOuS7Al/gbAS+KUHwiIlEpO6+Q1qkn0eLSZ3mh/UUUTv0AjjgCOneGzz4r8/VlDRCJpjHWIiJS+kpzZ+dcW+BYoAeAc2480BHYKwKxiYhEpaKrxPkpu3PXkedybO8XWHT1zT5hbtUKOnTwkwdLUNoAEa1Ci4hEn9KS5gVm9jLwBvDRto3Ouc3OuUfCHpmISJQqbpV4fVJ1rqh3ki/bGDYM5s+Hdu2gbVuYOhW2u3+ktAEi0TbGWkRESkmanXMXAvcBg5xz/4lcSCIi0a3UMdO77eaHoaxaBY8+CitXwkkn+dXnCRP+TJ5LGw0dbWOsRUSkjBsBnXPznXNLIhWMiEgsKNeY6ZQUPxBlxQp45hn49ls47TRf9zxuHF0P27/EASLRNsZaREQqMBFQRES80laJ/6FaNejVC77+GkaMgF9+8ZMGmzen65IZzOrXjlVZpzKrf/s/281V6PgiIhIRSppFRCpoh8ZMJyf7aYKLF8Orr/oyjQsugMaN/bTBwsKdO76IiIRVqcNNAMzsTeAFYJJzbmtEotqOhpuISNzZuhXeeguGDIF58yAtzY/nvuQSvzotIiKB2NHhJgBPARcAy8wsy8wOqfToREQSTZUqvkxj7lx45x3YZx/o3RsaNYLHHoOC+LzpT/2nRSRWlZk0O+fed851Bw4HcoGpZvaJmfU0s+RwBygiEtfM/hqIMnkypKfDtdf6P++/39dAxwn1nxaRWFaummYz2xu4BLgcyAEewSfRU8MWmYhIIjHzrelmzIAPP4SmTaFfP1+2cc898NNPQUe409R/WkRiWZlJs5mNAz4GagCnOee6OOfGOOeuAXYLd4AiIgmnXTt4/3345BM4+mgYONAnz7ffDhs2BB3dDpdYqP+0iMSy8qw0P+eca+KcG+qcWwdgZtUAiiuSFhGRStKqFUycCHPmwAknwF13Qf36MGAAfPddICHtTImF+k+LSCwrT9I8pJhtn1Z2ICIiUoLDD4dx4+Crr+DUU+Hee/3K8w03wLp1EQ1lZ0os1H9aRGJZiUmzme1nZkcAKWbW0swOD30cjy/VEBGRSGrWDF57zfd6PvtsP6Y7PR2uvhr++9+IhLAzJRbqPy0isazEPs1mdjH+5r9M4AvAQk/9DLzonBsXiQBBfZpFRIq1ciVkZfnhKAAXX+x7PTdsGLZTts6aRl4xCXLd1BRm9W8ftvOKiERKhfs0O+deBE4Eejvn2jvnTgh9nB7JhFlERErQoAEMHw7Ll/tR3S+/DBkZ0KMHLFkSllOqxEJEElV5JgLOcM61jVA8xdJKs8Si7Jw8hk1eytr8AuqkptCvY4Z+DS3htW6d7+389NNQUMCaf3VmQJMuzKy+f6X+DOpnW0TiWUkrzeVJmm8FCoAxwK/btjvnItb3SEmzxJptHQaK3jCVkpyk+k2JjPXrWXrzXdQd9Ty7bSpg8kHH8Nix57HigAz9DIqIlKGkpLlqOV57aejPq4tsc0CDyghMJB6V1mFACYuEXe3aXHrwGfzSuzU954yn5+zxdFz2GdMbHMHo7y+m61PXVPoptfosIvGuPGO004v5UMIsUgoNcZCgrc0v4KeU3Xn4uO607jOC+9r2oPm6ZQx/+lr417/81MEyftNYXhqPLSKJoDwTAWuY2SAzGx56fJCZdQ5/aCKxS0McJJzKM5Gv6M/aL9Vq8GSrcziu9ws8dsqVsHChH5bSti1MmbLTybPGY4tIIijPcJMRwCbg2NDjNRQ/8ORvzOwFM/vOzBYU2baXmU01s2WhP/fcoahFopw6DEi4lHdVt7ifQXbdlQOG3Opb1T32GOTmQseOcMwx8M47O5w86zcrIpIIypM0N3TO3QcUAjjnCvirZ3NpRgKdttvWH/jAOXcQ8EHosUjc0RAHCZfyruqW+jOYkgL//rdvVffMM34kd5cu0LIljB0LW7dWKCb9ZkVEEkF5bgTcZGYp+Jv/MLOGwB9lvcg5N8PM0rbbfDpwfOjzF4EPgZvLGatITOnasq6SZKl0FVnVLfNnsFo139+5Z0949VW45x4/abBJExg4EM45B6qW/c9Ev44ZxXaL0W9WRCSelGel+Q7gPeAAMxuFXyG+aQfPt69zbh1A6M99dvA4IiIJKSyrusnJfprgokU+eTaD7t2hcWMYMQIKC0t9eUmr2kCZtdciIrGizD7NAGa2N3AMvizjM+fc9+U6uF9pnuCcaxp6nO+cSy3y/I/OuWLrms2sF9AL4MADDzxi9erV5TmliEhci0gP8K1bITsbBg+GefOgfn0/nrtnT786HS1xioiEQYXHaBd54XjgJOBD59yE8ibMJfjWzPYPHXd/4LuSdnTODXfOZTrnMmvXrr0TpxQRiR8RqZevUgW6dYO5c/0NgvvuC336QMOG8OijUFD2DX7qqCEi8aY85RkPAG2ARWb2hpmdZWbVd/B844GLQ59fDLy9g8cREUlYXVvWZVb/9qzKOpVZ/duHb+XWDDp3hs8+863pGjSA666D9HQ/rvuXX0p8qTpqiEi8Kc9wk4+cc1fhJwAOB86hlBXibcxsNPApkGFma8zsMiAL6GBmy4AOocciIhLNzKBDB5gxww9FadYM+vWDtDS4+2746ad/vEQdNUQk3pRnpZlQ94wzgd7AkfjOF6Vyzp3vnNvfOZfsnKvnnHveOfeDc+5E59xBoT837Fz4IiISUe3awdSp8Mknvr/zoEG+5vm222DDX3+lq1e5iMSbMm8ENLMxwNH4Dhqv42ubK9bEcydlZma62bNnR/KUIiJRJzsnj2GTl7I2v4A6qSn065gR9pvqyjzn3LkwZAi89RbsthtcfTXccAPss08g8YqI7KySbgQsT9LcCZjqnNtS6o5hpKRZRBJdEN0oKnTOBQt8qcaYMVC9OvTuDX37Qp06YYktnIom+zVTkjGD/N8KlfiLJIgd7p6B78t8tZmNDX1cY2bJlR+iiIiUJIhuFBU6Z9OmMHo0LF7sh6I8+qi/cfDqq+G//w1bjJVt+zHl+QWF/PhbYakjy0UkMZQnaX4KOAJ4MvRxeGibiIhESBDdKMpzzuycPFpnTSOt/0QaDniXtBHLaX1ID6a8NcMPTHn2Wd+q7vLLYcWKsMVaWYr7j0JRapsnkrjKkzQf6Zy72Dk3LfTRE38zoIiIREgQ3SjKOmfRVVmALaFyv7z8Aq77v5/J7n2bT5R794ZXXoGMDOjRA5YsCVvMO6s8/wlR2zyRxFSepHmLmTXc9sDMGgCB1TeLiCSiILpRlHXO0lZl/1yRPeAAeOwxWLUKrr8e3nwTmjSBc8+F+fP/9pptq9ZBjt0uz39C1DZPJDGVJ2nuB0w3sw/N7CNgGnBjeMMSEZGiIjIJsILnLGvF9W/P77+/H4iSm+tHck+aBM2bwxlnwJw5/6glDqp+uLj/KBSltnkiiavM7hkAZlYNyAAMWOKc+yPcgRWl7hkiEq0Sua1a66xpf5ZmFKduagqz+rcv/skNG/wK9MMPQ34+nx58FMOOOpu5dRuX/xhhou4ZIoltZ1rOVQeuAo4DHPAx8LRz7vdwBFocJc0iEo2CaAMXTYr7+rcp9/fh55/hiSf4YXAWexf8zKz6zXns2PP47IBmYIYBq7JODc8XICJSjJ1pOfcScCjwGPA40AR4uXLDExGJPUG0gYsmRcs3AJLMgAqWjuyxBwwYwDn9X2XwCZdx0Pff8NroW3j91Ztps2oudWpWD+eXICJSblXLsU+Gc+6wIo+nm9mX4QpIRCRWBNEGLtp0bVm3UlbVrzmtBQMKk3il5Smc+9UUen/+Ji+/fhsbFrWApndB584QSspFRIJQnpXmHDM7ZtsDMzsamBW+kEREYkMQbeDi1bZV61q1U3n5iNM4/6ZXyBl0L3v9+hN06QItW8LYsbB1a9ChikiCKk9N82L8TYDbRjodCCwGtgLOOdc8rBGimmYRiU6JXtMcEYWF8OqrcM898PXXvl3dwIG+ZV1SyV0uRER21M7UNHcC0oF2oY904BSgM3BaZQYpIhJLgmgDl3CSk/1kwUWL/JhuM+jeHRo3hhEjfFItIhIB5Wo5FzStNIuICODLM95+GwYPhpwcSEvzfZ8vuQSqVQs6OhGJAzuz0iwiIhIdqlT5cyAKEybAvvv6Md0NG8Kjj8JvvwUdoYjEKSXNIiISe8zg1FPh009h6lSfNF93HaSnw7Bh8MsvQUcoInFGSbOISARk5+TROmsa6f0n0jprWsTHQ0dbHJXGDP71L/joI/9x2GFw002+bOPuu+Gnn4KOUETihJJmEZEw29ZlIy+/AAfk5RcwYNz8iCes0RJH2LRtC1OmwGefQatWMGgQ1K8Pt90GP/wQdHQiEuOUNIuIhFm0TA4MRxxRuXJ99NHwzjswdy6ceKK/aTAtDW6+Gb77LujoRCRGKWkWEQmzaJkcWNlxRP3KdcuW8OabsGABnHYa3H+/T57/8x/Ii5IYRSRmKGkWEQmzaJkcWNlxRMsKepkOPdQPSFm82A9FeewxaNAArroKVq8OOjoRiRFKmkVEwqxfxwxSkv8+vS4lOYl+HTNiOo5oWUEvt4MP9gNRli3zfZ2few4aNYLLLoPly4OOTkSinJJmEZEwi5bJgZUdR7SsoFdYejo88wysXAl9+vhV6IwMuOgivxotIlIMTQQUESlGdk4ewyYvZW1+AXVSU+jXMUPjsbezraa5aIlGSnJSWP5DEK7rkZ2Tx/NjP+W090dzUc67VN/8B3bWWb7zRvPmlRC5iMSakiYCKmkWEdlOJJPBWBeJ/1yE63psf9w9f/uJK+eO57J5E0n+9Rfo0gVuvRUy//Fvp4jEMSXNIiLl1DprGnnF1OXWTU1hVv/2AUSU2MJ1PUo67iHVNvNe0pfw8MPw44/QqZNPno89dofPJSKxo6SkWTXNIiLbibkb3OJcuK5HSa9f+kdVPxAlNxeGDoXZs6F1a2jfHqZPhxhYbBKRyqekWURkOzF7g1uAwjnkJFzXo8zj7rEH9O/vk+cHH4QlS3zi3KYNvPeekmeRBKOkWURkO9HSIi5WhHvISbiuR7mPu+uufiDKypXwxBPw3//CySf7yYPjxyt5FkkQgSTNZvYfM1toZgvMbLSZVQ8iDhGR4kRLi7hYEe4hJ+G6HhU+bvXqfiDK8uXw7LPwww9w+unQogW88QZs3bpT8YhIdIv4jYBmVheYCTRxzhWY2evAu865kSW9RjcCiohEr/T+EynuXxIDVmWdGulwImfzZhg9Gu6+G5YuhcaN4ZZb4LzzoGrVoKMTkR0UbTcCVgVSzKwqUANYG1AcIiKykxK2BrxqVT8QZeFCGDPmr8eNG8MLL8CmTUFHKCKVKOJJs3MuD7gf+C+wDvjJOTdl+/3MrJeZzTaz2evXr490mCIiUk4JXwOelATnnAPz5sFbb/kbCC+7DA46CJ56Cv74I+gIRaQSRDxpNrM9gdOBdKAOsKuZXbj9fs654c65TOdcZu3atSMdpojIDgtnJ4loPL9qwEOqVIGuXX2LuokToU4dXwPdoAE88gj89lvQEYrITgiipvlsoJNz7rLQ4x7AMc65q0p6jWqaRSRWBD1NMOjzSxHOwbRpMHgwfPQR7LMP3Hgj9OkDu+8edHQiUoJoqmn+L3CMmdUwMwNOBBYHEIeISKULdyeJaD+/FGEGJ54IH34IM2b4Lhs33wxpaT6Rzs8PNj4RqZAgapo/B8YCc4H5oRiGRzoOEZFwCHqaYNDnlxK0aQOTJ8Nnn/npgrfdBvXrw6BBvnWdiES9QLpnOOdud84d4pxr6py7yDmnuyREJC4E3Uki6PNLGbYNRMnJgQ4dfLu6+vXhppvg22+Djk5ESqGJgCIilSjoThJBn1/KqUULGDsWFizwA1IeeMCXbVx3HeRF9sZRESkfJc0iIpUo6E4SQZ9fKujQQ2HUKFi8GM4/H5580nfb6NMHcnODjk5Eioh494wdoe4ZIiKSEHJzISsLRozwY7kvushPGWzUKOjIRBJGNHXPEBERkeKkpcHTT8OKFb7H8+jRkJEBF14IixYFHZ1IQlPSLCISp4IesiI7oV49PxBl1Sq44QbIzoamTeHss+HLL4OOTiQhKWkWEYlD24ac5OUX4IC8/AIGjJuvxDnW7LcfDBvmyzZuuQWmTPE3EXbpAl98EXR0IglFSbOISBzSkJM4U6sWDBkCq1fDXXfBzJlw1FHQqZP/XETCTkmziEgc0pCTOJWaCrfe6pPnrCyYO9cPTjnhBD+yOwZu7heJVUqaRUTikIacxLndd/cjuVetgocegqVL/cju446DSZOUPIuEgZJmEZE4pCEnCWLXXeH662HlSnjiCfjmGzjlFF+68fbbvm2diFQKJc0iInFIQ04STPXqvkXd8uXw3HOwYQN07QotW8Lrr8OWLWUeQkRKp+EmIiIi8WbzZt/j+e67fenGIYf47hvnnw9VqwYdnUhU03ATERGRRFG1qp8muHAhjBkDycnQo4dPnp9/HjZtCjpCkZijpFlERCReJSXBOefAvHnw1ltQsyZcfjkcdBA8+ST8/nvQEYrEDCXNIiIi8a5KFV/jPHs2vPsu1K0LV18NDRr47hu//RZ0hCJRT0mziIhIojCDk0+GWbPg/ffh4IP9mO60NLj3Xti4MegIRaKWkmYREZFEY+b7On/4IcyY4bts9O8P9ev7iYP5+UFHKBJ1lDSLiIgksjZtYPJk+PxzPxzl9tt98jxoEHz/fdDRiUQNJc0iIiLiB6KMHw85OdChg29Xl5YG/frB//4XdHQigVPSLCIiIn9p0QLGjoUFC+D00+HBByE9Ha67DvLygo5OJDBKmkVERMIoOyeP1lnTSO8/kdZZ08jOiZHE89BDYdQoWLLED0V58knfbaN3b8jNDTo6kYhT0iwiIhIm2Tl5DBg3n7z8AhyQl1/AgHHzYydxBt/T+YUXYNky6NkTRozw2y691G8TSRBKmkVERMJk2OSlFBRu+du2gsItDJu8NKCIdkJaGjz9NKxYAVdd5cd0H3IIdO8OixYFHZ1I2ClpFhERCZO1+QUV2h4T6tWDRx7xJRo33ghvvw1Nm8LZZ/vJgyJxSkmziIhImNRJTanQ9piy775w330+eb7lFpgyxfd77tIF/u//go5OpNIpaRYREQmTfh0zSElO+tu2lOQk+nXMCCiiMKhVC4YMgdWr/WCUWbPg6KOhY0eYOTPo6EQqjZJmERGRMOnasi5DuzWjbmoKBtRNTWFot2Z0bVk36NAqX2oq3HqrX3m+917f77lNGzjhBJg2DZwLOkKRnWIuBn6IMzMz3ezZs4MOQ0RERMrrt99g+HBfwrFuHbRq5ZPqTp38GG+RKGVmc5xzmdtv10qziIiIVL4aNeD662HlSt/jOS8PTjkFjjwSsrNh69agIxSpkECSZjNLNbOxZrbEzBabWasg4hAREZEwq14d+vTxPZ2ffx7y8+GMM/zkwddfhy1byjqCSFQIaqX5EeA959whwGHA4oDiEBERkUjYZRc/EGXJEnj5ZSgshHPP9e3qXn4ZNm8OOkKRUkU8aTazPYC2wPMAzrlNzrn8SMchIiIiAahaFS68EBYs8CvNu+wCPXr4QSnPPw+bNgUdoUixglhpbgCsB0aYWY6ZPWdmu26/k5n1MrPZZjZ7/fr1kY9SREREwicpyQ9EycnxNc577gmXX+5HdD/5JPz+e9ARivxNEElzVeBw4CnnXEvgV6D/9js554Y75zKdc5m1a9eOdIwiIiISCVWqwOmn+4Eokyb5iYNXXw0NGsBDD/kuHCJRIIikeQ2wxjn3eejxWHwSLSIiIonKzLejmzkTPvjAl2vccAOkpfm+zxs3Bh2hJLiIJ83Ouf8B35jZtnFIJwKLIh2HiIiIRCEzaN/eD0SZORMOPxz694f69f3Ewfz8oCOUBBVU94xrgFFm9hXQArgnoDhEREQkWrVuDe+950s32rSB22/3yfPAgfD990FHJwlGEwFFRESiSHZOHsMmL2VtfgF1UlPo1zEjPsdu74gvv4QhQ+DNN/3wlD594MYbYb/9go5M4ogmAoqIiES57Jw8BoybT15+AQ7Iyy9gwLj5ZOfkBR1adDjsMHjjDd+urmtXePBBSE+Ha6+FNWuCjk7inJJmERGRKDFs8lIKCv8+Ia+gcAvDJi8NKKIo1aQJvPIKLF0KF1wATz3lu21ceSWsWhV0dBKnlDSLiIhEibX5BRXanvAaNfIDUZYtg8sug5EjfZ/nnj3h66+Djk7ijJJmERGRKFEnNaVC2yUkLc2vNq9cCf/+N7z2GjRu7FehFy4MOjqJE0qaRUREokS/jhmkJCf9bVtKchL9OmaU8Ar5m7p14eGHITcX+vaF8eOhaVM480w/eVBkJyhpFhERiRJdW9ZlaLdm1E1NwYC6qSkM7dZM3TMqat99/UCU1ath0CB4/33f7/m00+Dzz8t+vUgx1HJORERE4lt+Pjz+uB/LvWEDdOgAt97qez+LbEct50RERCQxpab6FefVq+G++3y/57ZtoV07vwodAwuIEjwlzSIiIpIYdtsN+vXzbekefhiWL/erzsceC+++q+RZSqWkWURERBJLjRpw3XW+28ZTT8G6dXDqqZCZCW+9BVu3Bh2hRCElzSIiIpKYqlWD3r19n+cXXoCff4Zu3fzkwTFjYMuWso8hCUNJs4iIiCS25GQ/EGXxYj9pcMsWOO88OPRQeOkl2Lw56AglCihpFhEREQGoWhW6d4cFC+CNN6B6dbj4YsjIgGefhU2bgo5QAqSkWURERKSoKlXgrLP8QJTx42HvvaFXLz+2+4kn4Pffg45QAqCkWURERKQ4Zn8NRHnvPTjwQD+mOz0dHnwQfv016AglgpQ0i4iIiJTGDDp2hI8/hunToUkTuPFGSEuDoUP9DYQS95Q0i4iIiJSHGRx/PHzwAcyaBUceCbfc4pPnO++EH38MOkIJIyXNIiIiIhW1bSDKF1/46YJ33AH16/skev36oKOTMFDSLCIiIrKjMjMhO9uP5j75ZMjK8ivPffv6oSkSN5Q0i4iIiOys5s39QJSFC+HMM/2Y7vR0uOYa+OaboKOTSqCkWURERKSyNG7sB6IsXQoXXghPPw0NG/qWdatWBR2d7AQlzSIiIiKVrWFDeO45WL4crrgCXnwRDjoILrnEJ9QSc5Q0i4iIiIRL/fp+IMqqVb5U4/XXfcu688/3kwclZihpFhEREQm3OnXgoYcgNxf69YMJE6BZM+jWzU8elKinpFlEREQkUvbZx3fYyM2FW2+FadPg8MOhc2c/eVCilpJmERERkUjbe2+46y5YvRqGDIFPP4VjjoEOHWDGjKCjk2IoaRYREREJSs2aMHCgT57vuw+++gratfMDU6ZOBeeCjlBClDSLiIiIBG233Xytc24uPPIIrFwJJ50ErVr5+mclz4FT0iwiIiISLVJS4NprYcUKeOop+N//4LTT4IgjYNw42Lo16AgTVmBJs5klmVmOmU0IKgYRERGRqFStGvTuDcuWwQsvwMaNftJg8+YwejRs2RJ0hAknyJXm64DFAZ5fREREJLolJ0PPnrB4MYwa5cs0LrjA93p+8UUoLAw6woQRSNJsZvWAU4Hngji/iIiISEypWtUny/Pnwxtv+DKOSy6BjAwYPhz++CPoCONeUCvNDwM3ASUW5phZLzObbWaz169fH7HARERERKJWlSpw1ll+IMr48VCrFlx5JTRqBI8/DgUFQUcYtyKeNJtZZ+A759yc0vZzzg13zmU65zJr164doehEREREYoCZv0Hw88/hvff8uO5rroEGDeCBB+DXX4OOMO4EsdLcGuhiZrnAa0B7M3slgDhEREREYpsZdOwIH38M06f7Wue+fSEtDYYOhZ9/DjrCuBHxpNk5N8A5V885lwacB0xzzl0Y6ThERERE4oYZHH88fPABzJoFRx4Jt9ziV6DvuAN+/DHoCGOe+jSLiIiIxJNjj4V334UvvvCJ9J13+uR5wADQfWI7LNCk2Tn3oXOuc5AxiIiIiMSlzEx46y348ks4+WS4915ftnHjjbBuXdDRxRytNIuIiIjEs+bNYcwYWLjQD0h55BFIT/c3Dn7zTdDRxQwlzSIiIiKJoHFjeOklWLoULrwQnn4aGjaEXr1g5cqgo4t6SppFREREEknDhvDcc7BiBVxxhZ8sePDBfljK0qVBRxe1lDSLiIiIJKIDD4QnnoBVq+Daa+H11/1q9Pnnw4IFQUcXdZQ0i4iIiCSyOnXgwQchNxduugkmTIBmzaBbN5g7N+joooaSZhERERGBffaBrCyfPN92G0ybBkccAZ07w2efBR1d4JQ0i4iIiMhf9t7b93ZevRqGDPEJc6tW0KEDzJgRdHSBUdIsIiIiIv9UsyYMHOhXnocNg/nzoV07aNsWpk4F54KOMKKUNIuIiIhIyXbbDfr29TcMPvKIb0930kl+9XnChIRJnpU0i4iIiEjZUlJ8l40VK3yP52+/hdNO83XP48bB1q1BRxhWSppFREREpPyqVYMrr4Svv4YRI+CXX/ykwebNYfRo2LIl6AjDQkmziIiIiFRccrIfiLJ4Mbz6qi/TuOAC3+t55EgoLAw6wkqlpFlEREREdlxSkh+IMn8+jB0Lu+4KPXtCRgYMHw5//BF0hJVCSbOIiIiI7LwqVXyZxty58M47ULu2L+No1AgeewwKCoKOcKcoaRYRERGRymP210CUKVMgPd3fQNigATzwgK+BjkFKmkVERESk8pn9NRDlww/h0EN967q0NLjnHvj556AjrBAlzSIiIiISXu3awfvvwyefwNFH+6Ep9evD7bfDhg1BR1cuSppFREREJDJatYKJE2HOHDjhBLjrLr/yPGAAfPdd0NGVSkmziIiIiETW4Yf7gShffQWnnAL33uuT5xtugHXrgo6uWEqaRURERCQYzZrBa6/5Xs9nnw2PPupvHLz66qjr86ykWURERESClZEBL77opwz26AErV/rhKVGkatABiIiIiIgAvi3d8OGwdWvQkfyDVppFREREJLpUib4UNfoiEhERERGJMkqaRURERETKoKRZRERERKQMSppFRERERMqgpFlEREREpAxKmkVEREREyhDxpNnMDjCz6Wa22MwWmtl1kY5BRERERKQighhushm40Tk318x2B+aY2VTn3KIAYhERERERKVPEV5qdc+ucc3NDn28EFgN1Ix2HiIiIiEh5BVrTbGZpQEvg8yDjEBEREREpTWBJs5ntBrwJXO+c+7mY53uZ2Wwzm71+/frIBygiIiIiEhJI0mxmyfiEeZRzblxx+zjnhjvnMp1zmbVr145sgCIiIiIiRZhzLrInNDPgRWCDc+76cr5mPbA6nHGVoBbwfQDnlcjSdU4Mus6JQdc5/ukaJ4Ygr3N959w/VmyDSJqPAz4G5gNbQ5tvcc69G9FAysHMZjvnMoOOQ8JL1zkx6DonBl3n+KdrnBii8TpHvOWcc24mYJE+r4iIiIjIjtJEQBERERGRMihpLt3woAOQiNB1Tgy6zolB1zn+6Ronhqi7zhGvaRYRERERiTVaaRYRERERKYOS5hAzyzCzeUU+fjaz683sDjPLK7L9lKBjlR1nZv8xs4VmtsDMRptZdTPby8ymmtmy0J97Bh2n7JwSrrPey3HGzK4LXeOFZnZ9aJvez3GmhOus93OMM7MXzOw7M1tQZFuJ718zG2Bmy81sqZl1DCRmlWf8k5klAXnA0UBP4Bfn3P3BRiU7y8zqAjOBJs65AjN7HXgXaILvG55lZv2BPZ1zNwcZq+y4Uq5zGnovxw0zawq8BhwFbALeA/oAV6D3c9wo5Tp3R+/nmGZmbYFfgJecc01D2+6jmPevmTUBRuN/DuoA7wMHO+e2RDJmrTQX70RghXMuiIEqEl5VgRQzqwrUANYCp+MH7hD6s2swoUklKu46S3xpDHzmnPvNObcZ+Ag4A72f401J11linHNuBrBhu80lvX9PB15zzv3hnFsFLMcn0BGlpLl45+H/R7PNv83sq9CvEvSrvhjlnMsD7gf+C6wDfnLOTQH2dc6tC+2zDtgnuChlZ5VynUHv5XiyAGhrZnubWQ3gFOAA9H6ONyVdZ9D7OR6V9P6tC3xTZL81oW0RpaR5O2a2C9AFeCO06SmgIdAC/w/wA8FEJjsr9Jfq6UA6/tc7u5rZhcFGJZWtlOus93Iccc4tBu4FpuJ/Zf8lsDnQoKTSlXKd9X5OLMUNxYt4fbGS5n86GZjrnPsWwDn3rXNui3NuK/AsAfw6QCrNv4BVzrn1zrlCYBxwLPCtme0PEPrzuwBjlJ1X7HXWezn+OOeed84d7pxri/817zL0fo47xV1nvZ/jVknv3zX89RsGgHoEUHanpPmfzqdIaca2ixdyBv5XRRKb/gscY2Y1zMzwteuLgfHAxaF9LgbeDig+qRzFXme9l+OPme0T+vNAoBv+7269n+NMcddZ7+e4VdL7dzxwnplVM7N04CDg/yIdnLpnFBGql/oGaOCc+ym07WX8r38ckAtcua3eRmKPmd0JnIv/9V4OcDmwG/A6cCA+4TrbObf9zQkSQ0q4zs+h93JcMbOPgb2BQuAG59wHZrY3ej/HlRKus/5tjnFmNho4HqgFfAvcDmRTwvvXzAYCl+L/Xr/eOTcp4jEraRYRERERKZ3KM0REREREyqCkWURERESkDEqaRURERETKoKRZRERERKQMSppFRERERMqgpFlEREREpAxKmkVEIszM0swsqoYxmNnxZjahmO2tzewrM/vCzBqFtqWa2eTQ8BgRkYSgpFlEJE6Zt7N/z98InAncAvQJbbsVuMep0b+IJBAlzSIiwUgys2fNbKGZTTGzFAAzu9bMFoVWd18r6cVmVtvMpprZXDN7xsxWm1mt0Cr2YjN7EpgLHGBmT5nZ7NC57ixyjE5mtsTMZuLHExenEEgBagCFZtYQqOuc+6iyvhEiIrFAEwFFRCLMzNKA5UCmc26emb0OjHfOvWJma4F059wfZpbqnMsv4RiPA3nOuaFm1gmYBNTGj4VfCRzrnPsstO9ezrkNZpYEfABcC3wNLAPah2IZA9RwznXe7jwtgKeBAuAi4H7gVufcssr7joiIRD+tNIuIBGOVc25e6PM5QFro86+AUWZ2IbC5lNcfB7wG4Jx7D/ixyHOrtyXMIeeY2VwgBzgUaAIcEophWajM4pXiTuKcm+ecO8Y5dwLQAFiLr/wYY2avmNm+5f6KRURimJJmEZFg/FHk8y1A1dDnpwJPAEcAc8ys6vYvDCntJrxf/9zJLB3oC5zonGsOTASqh54u968aQzf9DQIGA7eHPl7Br1qLiMQ9Jc0iIlEidNPeAc656cBNQCq+3KI4M4FzQq87CdizhP32wCfRP4VWhU8ObV8CpIdqlAHOLyO8i4GJzrkf8fXNW0MfNcp4nYhIXChpBUNERCIvCXjFzGriV5IfKqmmGbgTGG1m5wIfAeuAjWyXZDvnvjSzHGAhvtZ5Vmj772bWC5hoZt/jk/CmxZ3IzGrgk+aTQpseBN4ENlF2si0iEhd0I6CISAwys2rAFufcZjNrBTzlnGsRcFgiInFLK80iIrHpQOD1UEnHJuCKgOMREYlrWmkWEYliZtYTuG67zbOcc1cHEY+ISKJS0iwiIiIiUgZ1zxARERERKYOSZhERERGRMihpFhEREREpg5JmEREREZEyKGkWERERESnD/wNRXGzwSV6b0wAAAABJRU5ErkJggg==\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "'''Построим модель'''\n", - "from scipy.stats import linregress\n", - "\n", - "slope, intercept, r, p, std_err = linregress(df['hs_grad'], df['poverty'])\n", - "\n", - "x = np.linspace(75, 100)\n", - "\n", - "reg = lambda x: intercept + slope*x\n", - "plt.scatter(x='hs_grad', y='poverty', data=df, label='data')\n", - "plt.xlabel('hs_grad %')\n", - "plt.ylabel('poverty %')\n", - "plt.title('Linear Regression')\n", - "plt.plot(x, reg(x), color='r', label='fitted line')\n", - "plt.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "slope = -0.62\n", - "intercept = 64.78\n", - "r = -0.75\n", - "r squared = 0.56\n", - "p = 0.00000\n", - "std_err = 0.079\n", - "\n" - ] - } - ], - "source": [ - "print(f'''\n", - "slope = {slope:.2f}\n", - "intercept = {intercept:.2f}\n", - "r = {r:.2f}\n", - "r squared = {(r ** 2):.2f}\n", - "p = {p:.5f}\n", - "std_err = {std_err:.3f}\n", - "''')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Задача предсказания значений зависимой переменной" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Регрессионный анализ с несколькими независимыми переменными\n", - "\n", - "### Множественная регрессия (Multiple Regression)\n", - "\n", - "Множественная регрессия позволяет исследовать влияние сразу нескольких независимых переменных на одну зависиммую.\n", - "\n", - "#### Требования к данным\n", - "\n", - "- линейная зависимость переменных\n", - "- нормальное распредление остатков\n", - "- гомоскедастичность данных\n", - "- проверка на мультиколлиарность\n", - "- нормальное распределение переменных (желательно)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Пример расчёта и визуализации множественной регрессии" - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - " \n", - " " - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "application/vnd.plotly.v1+json": { - "config": { - "plotlyServerURL": "https://plot.ly" - }, - "data": [ - { - "hovertemplate": "poverty_pred=False
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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import pandas as pd\n", - "import plotly.express as px\n", - "import plotly.graph_objects as go\n", - "import numpy as np\n", - "import statsmodels.formula.api as smf\n", - "\n", - "df = pd.read_csv('data/states.csv')\n", - "\n", - "# Построим плоскость предсказания\n", - "lm = smf.ols(formula='poverty ~ white + hs_grad', data=df).fit()\n", - "mesh_size = 1.0\n", - "margin = 2.0\n", - "x_min, x_max = df.white.min()- margin, df.white.max() + margin\n", - "y_min, y_max = df.hs_grad.min()- margin, df.hs_grad.max() + margin\n", - "z_pred = lambda x, y: lm.params.white * x + lm.params.hs_grad * y + lm.params.Intercept\n", - "x_range = np.arange(x_min, x_max, mesh_size)\n", - "y_range = np.arange(y_min, y_max, mesh_size)\n", - "z_range = np.array([[z_pred(x, y) for x in x_range] for y in y_range])\n", - "\n", - "# какие значения выше предсказания, а какие ниже\n", - "df['poverty_pred'] = np.array([poverty >= z_pred(df.white[i], df.hs_grad[i]) for i, poverty in df.poverty.items()])\n", - "\n", - "# составим график\n", - "fig = px.scatter_3d(df, x='white', y='hs_grad', z='poverty',\n", - " color='poverty_pred', color_discrete_sequence=['red', 'green'],\n", - " title='зависиость процента белого населения и уровня образования на бедность населения')\n", - "fig.update_traces(marker=dict(size=3))\n", - "fig.add_traces(go.Surface(x=x_range,y=y_range, z=z_range, name='prediction', opacity=0.8))\n", - "fig.show()\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "** сверху должен быть объёмный график, но если его не видно, запустите этот код у себя на компе" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Выбор наилучшей модели\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Классификация: логистическая регрессия и кластерный анализ" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "# Полезные ссылки\n", - "\n", - "- https://gallery.shinyapps.io/dist_calc/\n", - " - сайт где можно визуализировать различные распределения и вести подсчёты" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.8.5" - } - }, - "nbformat": 4, - "nbformat_minor": 4 -}