{"id":1322,"date":"2023-07-26T21:04:15","date_gmt":"2023-07-26T21:04:15","guid":{"rendered":"https:\/\/statorials.org\/uk\/%d0%ba%d0%b2%d0%b0%d0%bd%d1%82%d0%b8%d0%bb%d1%8c%d0%bd%d0%b0-%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81%d1%96%d1%8f-%d0%b2-python\/"},"modified":"2023-07-26T21:04:15","modified_gmt":"2023-07-26T21:04:15","slug":"%d0%ba%d0%b2%d0%b0%d0%bd%d1%82%d0%b8%d0%bb%d1%8c%d0%bd%d0%b0-%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81%d1%96%d1%8f-%d0%b2-python","status":"publish","type":"post","link":"https:\/\/statorials.org\/uk\/%d0%ba%d0%b2%d0%b0%d0%bd%d1%82%d0%b8%d0%bb%d1%8c%d0%bd%d0%b0-%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81%d1%96%d1%8f-%d0%b2-python\/","title":{"rendered":"\u042f\u043a \u0432\u0438\u043a\u043e\u043d\u0430\u0442\u0438 \u043a\u0432\u0430\u043d\u0442\u0438\u043b\u044c\u043d\u0443 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u044e \u0432 python"},"content":{"rendered":"

<\/p>\n

\n

\u041b\u0456\u043d\u0456\u0439\u043d\u0430 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u044f \u2013 \u0446\u0435 \u043c\u0435\u0442\u043e\u0434, \u044f\u043a\u0438\u0439 \u043c\u0438 \u043c\u043e\u0436\u0435\u043c\u043e \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u0430\u0442\u0438 \u0434\u043b\u044f \u0440\u043e\u0437\u0443\u043c\u0456\u043d\u043d\u044f \u0437\u0432\u2019\u044f\u0437\u043a\u0443 \u043c\u0456\u0436 \u043e\u0434\u043d\u0456\u0454\u044e \u0430\u0431\u043e \u0434\u0435\u043a\u0456\u043b\u044c\u043a\u043e\u043c\u0430 \u0437\u043c\u0456\u043d\u043d\u0438\u043c\u0438 \u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u0430 \u0442\u0430 \u0437\u043c\u0456\u043d\u043d\u043e\u044e \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0456<\/a> .<\/span><\/p>\n

\u042f\u043a \u043f\u0440\u0430\u0432\u0438\u043b\u043e, \u043a\u043e\u043b\u0438 \u043c\u0438 \u0432\u0438\u043a\u043e\u043d\u0443\u0454\u043c\u043e \u043b\u0456\u043d\u0456\u0439\u043d\u0443 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u044e, \u043c\u0438 \u0445\u043e\u0447\u0435\u043c\u043e \u043e\u0446\u0456\u043d\u0438\u0442\u0438 \u0441\u0435\u0440\u0435\u0434\u043d\u0454 \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u0437\u043c\u0456\u043d\u043d\u043e\u0457 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0456.<\/span><\/p>\n

\u041e\u0434\u043d\u0430\u043a \u0437\u0430\u043c\u0456\u0441\u0442\u044c \u0446\u044c\u043e\u0433\u043e \u043c\u0438 \u043c\u043e\u0433\u043b\u0438 \u0431 \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u0430\u0442\u0438 \u043c\u0435\u0442\u043e\u0434, \u0432\u0456\u0434\u043e\u043c\u0438\u0439 \u044f\u043a \u043a\u0432\u0430\u043d\u0442\u0438\u043b\u044c\u043d\u0430 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u044f<\/strong> , \u0449\u043e\u0431 \u043e\u0446\u0456\u043d\u0438\u0442\u0438 \u0431\u0443\u0434\u044c-\u044f\u043a\u0435<\/em> \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u043a\u0432\u0430\u043d\u0442\u0438\u043b\u044f \u0430\u0431\u043e \u043f\u0440\u043e\u0446\u0435\u043d\u0442\u0438\u043b\u044f \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0456, \u043d\u0430\u043f\u0440\u0438\u043a\u043b\u0430\u0434 70-\u0439 \u043f\u0440\u043e\u0446\u0435\u043d\u0442\u0438\u043b\u044c, 90-\u0439 \u043f\u0440\u043e\u0446\u0435\u043d\u0442\u0438\u043b\u044c, 98-\u0439 \u043f\u0440\u043e\u0446\u0435\u043d\u0442\u0438\u043b\u044c \u0442\u043e\u0449\u043e.<\/span><\/p>\n

\u0426\u0435\u0439 \u043f\u0456\u0434\u0440\u0443\u0447\u043d\u0438\u043a \u043c\u0456\u0441\u0442\u0438\u0442\u044c \u043f\u043e\u043a\u0440\u043e\u043a\u043e\u0432\u0438\u0439 \u043f\u0440\u0438\u043a\u043b\u0430\u0434 \u0442\u043e\u0433\u043e, \u044f\u043a \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u0446\u044e \u0444\u0443\u043d\u043a\u0446\u0456\u044e \u0434\u043b\u044f \u0432\u0438\u043a\u043e\u043d\u0430\u043d\u043d\u044f \u043a\u0432\u0430\u043d\u0442\u0438\u043b\u044c\u043d\u043e\u0457 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457 \u0432 Python.<\/span><\/p>\n

\u041a\u0440\u043e\u043a 1: \u0417\u0430\u0432\u0430\u043d\u0442\u0430\u0436\u0442\u0435 \u043d\u0435\u043e\u0431\u0445\u0456\u0434\u043d\u0456 \u043f\u0430\u043a\u0435\u0442\u0438<\/strong><\/span><\/h3>\n

\u0421\u043f\u043e\u0447\u0430\u0442\u043a\u0443 \u043c\u0438 \u0437\u0430\u0432\u0430\u043d\u0442\u0430\u0436\u0438\u043c\u043e \u043d\u0435\u043e\u0431\u0445\u0456\u0434\u043d\u0456 \u043f\u0430\u043a\u0435\u0442\u0438 \u0442\u0430 \u0444\u0443\u043d\u043a\u0446\u0456\u0457:<\/span><\/p>\n

 import<\/span> numpy as<\/span> np\nimport<\/span> pandas as<\/span> pd\nimport<\/span> statsmodels. api<\/span> as<\/span> sm\nimport<\/span> statsmodels. formula<\/span> . api<\/span> as<\/span> smf\nimport<\/span> matplotlib. pyplot<\/span> as<\/span> plt\n<\/strong><\/pre>\n
 \u041a\u0440\u043e\u043a 2: \u0421\u0442\u0432\u043e\u0440\u0456\u0442\u044c \u0434\u0430\u043d\u0456<\/strong><\/span><\/h3>\n
 \u0414\u043b\u044f \u0446\u044c\u043e\u0433\u043e \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u0443 \u043c\u0438 \u0441\u0442\u0432\u043e\u0440\u0438\u043c\u043e \u043d\u0430\u0431\u0456\u0440 \u0434\u0430\u043d\u0438\u0445, \u044f\u043a\u0438\u0439 \u043c\u0456\u0441\u0442\u0438\u0442\u0438\u043c\u0435 \u043a\u0456\u043b\u044c\u043a\u0456\u0441\u0442\u044c \u0432\u0438\u0432\u0447\u0435\u043d\u0438\u0445 \u0433\u043e\u0434\u0438\u043d \u0456 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0438 \u0456\u0441\u043f\u0438\u0442\u0456\u0432, \u043e\u0442\u0440\u0438\u043c\u0430\u043d\u0456 \u0434\u043b\u044f 100 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0456\u0432 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0443:<\/span><\/p>\n
 #make this example reproducible\n<\/span>n.p. random<\/span> . seeds<\/span> (0)\n\n#create dataset\n<\/span>obs = 100\n\nhours = np. random<\/span> . uniform<\/span> (1, 10, obs)\nscore = 60 + 2*hours + np. random<\/span> . normal<\/span> (loc=0, scale=.45*hours, size=100)\n\ndf = pd. DataFrame<\/span> ({' hours<\/span> ':hours, ' score<\/span> ':score})\n\n#view first five rows\n<\/span>df. head<\/span> ()\n\nhours score\n0 5.939322 68.764553\n1 7.436704 77.888040\n2 6.424870 74.196060\n3 5.903949 67.726441\n4 4.812893 72.849046<\/strong><\/pre>\n
 \u041a\u0440\u043e\u043a 3: \u0412\u0438\u043a\u043e\u043d\u0430\u0439\u0442\u0435 \u043a\u0432\u0430\u043d\u0442\u0438\u043b\u044c\u043d\u0443 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u044e<\/strong><\/span><\/h3>\n
 \u0414\u0430\u043b\u0456 \u043c\u0438 \u043f\u0456\u0434\u0456\u0431\u2019\u0454\u043c\u043e \u043c\u043e\u0434\u0435\u043b\u044c \u043a\u0432\u0430\u043d\u0442\u0438\u043b\u044c\u043d\u043e\u0457 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457, \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u044e\u0447\u0438 \u0432\u0438\u0432\u0447\u0435\u043d\u0456 \u0433\u043e\u0434\u0438\u043d\u0438 \u044f\u043a \u0437\u043c\u0456\u043d\u043d\u0443 \u043f\u0440\u043e\u0433\u043d\u043e\u0441\u0442\u0438\u043a\u0443 \u0442\u0430 \u043e\u0446\u0456\u043d\u043a\u0438 \u0437\u0430 \u0456\u0441\u043f\u0438\u0442 \u044f\u043a \u0437\u043c\u0456\u043d\u043d\u0443 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0456.<\/span><\/p>\n
 \u041c\u0438 \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u0430\u0454\u043c\u043e \u0446\u044e \u043c\u043e\u0434\u0435\u043b\u044c, \u0449\u043e\u0431 \u043f\u0435\u0440\u0435\u0434\u0431\u0430\u0447\u0438\u0442\u0438 \u043e\u0447\u0456\u043a\u0443\u0432\u0430\u043d\u0438\u0439 90-\u0439 \u043f\u0440\u043e\u0446\u0435\u043d\u0442\u0438\u043b\u044c \u0456\u0441\u043f\u0438\u0442\u043e\u0432\u0438\u0445 \u0431\u0430\u043b\u0456\u0432 \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0456 \u043a\u0456\u043b\u044c\u043a\u043e\u0441\u0442\u0456 \u0432\u0438\u0432\u0447\u0435\u043d\u0438\u0445 \u0433\u043e\u0434\u0438\u043d:<\/span><\/p>\n
 #fit the model<\/span>\nmodel = smf. quantreg<\/span> ('score~hours', df). fit<\/span> (q= 0.9<\/span> )\n\n#view model summary\n<\/span>print<\/span> ( model.summary<\/span> ())\n\n                         QuantReg Regression Results                          \n==================================================== ============================\nDept. Variable: Pseudo R-squared score: 0.6057\nModel: QuantReg Bandwidth: 3.822\nMethod: Least Squares Sparsity: 10.85\nDate: Tue, 29 Dec 2020 No. Observations: 100\nTime: 15:41:44 Df Residuals: 98\n                                        Model: 1\n==================================================== ============================\n                 coef std err t P>|t| [0.025 0.975]\n-------------------------------------------------- ----------------------------\nIntercept 59.6104 0.748 79.702 0.000 58.126 61.095\nhours 2.8495 0.128 22.303 0.000 2.596 3.103\n==================================================== ============================<\/strong><\/span><\/pre>\n
 \u0417 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0443 \u043c\u0438 \u043c\u043e\u0436\u0435\u043c\u043e \u043f\u043e\u0431\u0430\u0447\u0438\u0442\u0438 \u043e\u0446\u0456\u043d\u0435\u043d\u0435 \u0440\u0456\u0432\u043d\u044f\u043d\u043d\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457:<\/span><\/p>\n
 90-\u0439 \u043f\u0440\u043e\u0446\u0435\u043d\u0442\u0438\u043b\u044c \u043e\u0446\u0456\u043d\u043a\u0438 \u0437\u0430 \u0456\u0441\u043f\u0438\u0442 = 59,6104 + 2,8495*(\u0433\u043e\u0434\u0438\u043d\u0438)<\/span><\/p>\n
 \u041d\u0430\u043f\u0440\u0438\u043a\u043b\u0430\u0434, 90-\u0439 \u043f\u0440\u043e\u0446\u0435\u043d\u0442\u0438\u043b\u044c \u0443\u0441\u0456\u0445 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0456\u0432, \u044f\u043a\u0456 \u043d\u0430\u0432\u0447\u0430\u044e\u0442\u044c\u0441\u044f 8 \u0433\u043e\u0434\u0438\u043d, \u043c\u0430\u0454 \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0438 82,4:<\/span><\/p>\n
 90-\u0439 \u043f\u0440\u043e\u0446\u0435\u043d\u0442\u0438\u043b\u044c \u0456\u0441\u043f\u0438\u0442\u043e\u0432\u043e\u0433\u043e \u0431\u0430\u043b\u0443 = 59,6104 + 2,8495*(8) = 82,4<\/strong> .<\/span><\/p>\n
 \u0412\u0438\u0445\u0456\u0434\u043d\u0456 \u0434\u0430\u043d\u0456 \u0442\u0430\u043a\u043e\u0436 \u0432\u0456\u0434\u043e\u0431\u0440\u0430\u0436\u0430\u044e\u0442\u044c \u0432\u0435\u0440\u0445\u043d\u044e \u0442\u0430 \u043d\u0438\u0436\u043d\u044e \u043c\u0435\u0436\u0456 \u0434\u043e\u0441\u0442\u043e\u0432\u0456\u0440\u043d\u043e\u0441\u0442\u0456 \u0434\u043b\u044f \u043f\u0435\u0440\u0435\u0445\u043e\u043f\u043b\u0435\u043d\u043d\u044f \u0442\u0430 \u0447\u0430\u0441\u0456\u0432 \u0437\u043c\u0456\u043d\u043d\u043e\u0457 \u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u0430.<\/span><\/p>\n
 \u041a\u0440\u043e\u043a 4: \u0412\u0456\u0437\u0443\u0430\u043b\u0456\u0437\u0443\u0439\u0442\u0435 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0438<\/strong><\/span><\/h3>\n
 \u041c\u0438 \u0442\u0430\u043a\u043e\u0436 \u043c\u043e\u0436\u0435\u043c\u043e \u0432\u0456\u0437\u0443\u0430\u043b\u0456\u0437\u0443\u0432\u0430\u0442\u0438 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0438 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457, \u0441\u0442\u0432\u043e\u0440\u0438\u0432\u0448\u0438 \u0434\u0456\u0430\u0433\u0440\u0430\u043c\u0443 \u0440\u043e\u0437\u0441\u0456\u044e\u0432\u0430\u043d\u043d\u044f \u0437 \u043f\u0456\u0434\u0456\u0433\u043d\u0430\u043d\u0438\u043c \u043a\u0432\u0430\u043d\u0442\u0438\u043b\u044c\u043d\u0438\u043c \u0440\u0456\u0432\u043d\u044f\u043d\u043d\u044f\u043c \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457, \u043d\u0430\u043a\u043b\u0430\u0434\u0435\u043d\u0438\u043c \u043d\u0430 \u0433\u0440\u0430\u0444\u0456\u043a:<\/span> <\/p>\n
 #define figure and axis\n<\/span>fig, ax = plt.subplots(figsize=(8, 6))\n\n#get y values\n<\/span>get_y = lambda<\/span> a, b: a + b * hours\ny = get_y( model.params<\/span> [' Intercept<\/span> '], model.params<\/span> [' hours<\/span> '])\n\n#plot data points with quantile regression equation overlaid\n<\/span>ax. plot<\/span> (hours, y, color=' black<\/span> ')\nax. scatter<\/span> (hours, score, alpha=.3)\nax. set_xlabel<\/span> (' Hours Studied<\/span> ', fontsize=14)\nax. set_ylabel<\/span> (' Exam Score<\/span> ', fontsize=14)\n<\/strong><\/span><\/pre>\n
\"\u041a\u0432\u0430\u043d\u0442\u0438\u043b\u044c\u043d\u0430<\/p>\n
 \u041d\u0430 \u0432\u0456\u0434\u043c\u0456\u043d\u0443 \u0432\u0456\u0434 \u043f\u0440\u043e\u0441\u0442\u043e\u0457 \u043b\u0456\u043d\u0456\u0457 \u043b\u0456\u043d\u0456\u0439\u043d\u043e\u0457 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457, \u0437\u0430\u0443\u0432\u0430\u0436\u0442\u0435, \u0449\u043e \u0446\u044f \u043f\u0456\u0434\u0456\u0431\u0440\u0430\u043d\u0430 \u043b\u0456\u043d\u0456\u044f \u043d\u0435 \u0454 \u00ab\u043b\u0456\u043d\u0456\u0454\u044e \u043d\u0430\u0439\u043a\u0440\u0430\u0449\u043e\u0433\u043e \u043f\u0456\u0434\u0445\u043e\u0434\u0443\u00bb \u0434\u043b\u044f \u0434\u0430\u043d\u0438\u0445. \u041d\u0430\u0442\u043e\u043c\u0456\u0441\u0442\u044c \u0432\u0456\u043d \u043f\u0440\u043e\u0445\u043e\u0434\u0438\u0442\u044c \u0447\u0435\u0440\u0435\u0437 \u0440\u043e\u0437\u0440\u0430\u0445\u0443\u043d\u043a\u043e\u0432\u0438\u0439 90-\u0439 \u043f\u0440\u043e\u0446\u0435\u043d\u0442\u0438\u043b\u044c \u043d\u0430 \u043a\u043e\u0436\u043d\u043e\u043c\u0443 \u0440\u0456\u0432\u043d\u0456 \u0437\u043c\u0456\u043d\u043d\u043e\u0457 \u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u0430.<\/span><\/p>\n
 \u0414\u043e\u0434\u0430\u0442\u043a\u043e\u0432\u0456 \u0440\u0435\u0441\u0443\u0440\u0441\u0438<\/strong><\/span><\/h3>\n
 \u042f\u043a \u0432\u0438\u043a\u043e\u043d\u0430\u0442\u0438 \u043f\u0440\u043e\u0441\u0442\u0443 \u043b\u0456\u043d\u0456\u0439\u043d\u0443 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u044e \u0432 Python<\/a>
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\u041b\u0456\u043d\u0456\u0439\u043d\u0430 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u044f \u2013 \u0446\u0435 \u043c\u0435\u0442\u043e\u0434, \u044f\u043a\u0438\u0439 \u043c\u0438 \u043c\u043e\u0436\u0435\u043c\u043e \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u0430\u0442\u0438 \u0434\u043b\u044f \u0440\u043e\u0437\u0443\u043c\u0456\u043d\u043d\u044f \u0437\u0432\u2019\u044f\u0437\u043a\u0443 \u043c\u0456\u0436 \u043e\u0434\u043d\u0456\u0454\u044e \u0430\u0431\u043e \u0434\u0435\u043a\u0456\u043b\u044c\u043a\u043e\u043c\u0430 \u0437\u043c\u0456\u043d\u043d\u0438\u043c\u0438 \u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u0430 \u0442\u0430 \u0437\u043c\u0456\u043d\u043d\u043e\u044e \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0456 . \u042f\u043a \u043f\u0440\u0430\u0432\u0438\u043b\u043e, \u043a\u043e\u043b\u0438 \u043c\u0438 \u0432\u0438\u043a\u043e\u043d\u0443\u0454\u043c\u043e \u043b\u0456\u043d\u0456\u0439\u043d\u0443 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