{"id":4057,"date":"2023-07-13T21:08:59","date_gmt":"2023-07-13T21:08:59","guid":{"rendered":"https:\/\/statorials.org\/uk\/%d0%bf%d0%be%d0%bb%d1%96%d0%bd%d0%be%d0%bc%d1%96%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0-%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81%d1%96%d1%8f-sklearn\/"},"modified":"2023-07-13T21:08:59","modified_gmt":"2023-07-13T21:08:59","slug":"%d0%bf%d0%be%d0%bb%d1%96%d0%bd%d0%be%d0%bc%d1%96%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0-%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81%d1%96%d1%8f-sklearn","status":"publish","type":"post","link":"https:\/\/statorials.org\/uk\/%d0%bf%d0%be%d0%bb%d1%96%d0%bd%d0%be%d0%bc%d1%96%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0-%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81%d1%96%d1%8f-sklearn\/","title":{"rendered":"\u042f\u043a \u0432\u0438\u043a\u043e\u043d\u0430\u0442\u0438 \u043f\u043e\u043b\u0456\u043d\u043e\u043c\u0456\u0430\u043b\u044c\u043d\u0443 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u044e \u0437\u0430 \u0434\u043e\u043f\u043e\u043c\u043e\u0433\u043e\u044e scikit-learn"},"content":{"rendered":"

<\/p>\n

\n

\u041f\u043e\u043b\u0456\u043d\u043e\u043c\u0456\u0430\u043b\u044c\u043d\u0430 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u044f<\/a> \u2014 \u0446\u0435 \u0442\u0435\u0445\u043d\u0456\u043a\u0430, \u044f\u043a\u0443 \u043c\u0438 \u043c\u043e\u0436\u0435\u043c\u043e \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438, \u043a\u043e\u043b\u0438 \u0437\u0432\u2019\u044f\u0437\u043e\u043a \u043c\u0456\u0436 \u0437\u043c\u0456\u043d\u043d\u043e\u044e \u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u043e\u043c \u0456 \u0437\u043c\u0456\u043d\u043d\u043e\u044e \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0456<\/a> \u043d\u0435\u043b\u0456\u043d\u0456\u0439\u043d\u0438\u0439.<\/span><\/p>\n

\u0426\u0435\u0439 \u0442\u0438\u043f \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457 \u043c\u0430\u0454 \u0432\u0438\u0433\u043b\u044f\u0434:<\/span><\/p>\n

Y = \u03b2 0<\/sub> +<\/sup> \u03b2 1<\/sub> X + \u03b2 2<\/sub> X 2<\/sup> + \u2026 + \u03b2 h<\/sub><\/span><\/p>\n

\u0434\u0435 h<\/em> \u2013 \u00ab\u0441\u0442\u0443\u043f\u0456\u043d\u044c\u00bb \u043f\u043e\u043b\u0456\u043d\u043e\u043c\u0430.<\/span><\/p>\n

\u041d\u0430\u0441\u0442\u0443\u043f\u043d\u0438\u0439 \u043f\u043e\u043a\u0440\u043e\u043a\u043e\u0432\u0438\u0439 \u043f\u0440\u0438\u043a\u043b\u0430\u0434 \u043f\u043e\u043a\u0430\u0437\u0443\u0454, \u044f\u043a \u0432\u0438\u043a\u043e\u043d\u0430\u0442\u0438 \u043f\u043e\u043b\u0456\u043d\u043e\u043c\u0456\u0430\u043b\u044c\u043d\u0443 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u044e \u0432 Python \u0437\u0430 \u0434\u043e\u043f\u043e\u043c\u043e\u0433\u043e\u044e sklearn.<\/span><\/p>\n

\u041a\u0440\u043e\u043a 1: \u0421\u0442\u0432\u043e\u0440\u0456\u0442\u044c \u0434\u0430\u043d\u0456<\/strong><\/span><\/h2>\n

\u0421\u043f\u043e\u0447\u0430\u0442\u043a\u0443 \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u0441\u0442\u0432\u043e\u0440\u0438\u043c\u043e \u0434\u0432\u0430 \u043c\u0430\u0441\u0438\u0432\u0438 NumPy \u0434\u043b\u044f \u0437\u0431\u0435\u0440\u0456\u0433\u0430\u043d\u043d\u044f \u0437\u043d\u0430\u0447\u0435\u043d\u044c \u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u0430 \u0442\u0430 \u0437\u043c\u0456\u043d\u043d\u043e\u0457 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0456:<\/span> <\/p>\n

 import<\/span> matplotlib. pyplot<\/span> as<\/span> plt\nimport<\/span> numpy as<\/span> np\n\n#define predictor and response variables\n<\/span>x = np. array<\/span> ([2, 3, 4, 5, 6, 7, 7, 8, 9, 11, 12])\ny = np. array<\/span> ([18, 16, 15, 17, 20, 23, 25, 28, 31, 30, 29])\n\n#create scatterplot to visualize relationship between x and y\n<\/span>plt. scatter<\/span> (x,y)\n<\/strong><\/pre>\n
\"\"<\/p>\n
 \u0417 \u0434\u0456\u0430\u0433\u0440\u0430\u043c\u0438 \u0440\u043e\u0437\u0441\u0456\u044e\u0432\u0430\u043d\u043d\u044f \u043c\u0438 \u0431\u0430\u0447\u0438\u043c\u043e, \u0449\u043e \u0437\u0430\u043b\u0435\u0436\u043d\u0456\u0441\u0442\u044c \u043c\u0456\u0436 x \u0456 y \u043d\u0435 \u0454 \u043b\u0456\u043d\u0456\u0439\u043d\u043e\u044e.<\/span><\/p>\n
 \u0422\u043e\u043c\u0443 \u0433\u0430\u0440\u043d\u043e\u044e \u0456\u0434\u0435\u0454\u044e \u0431\u0443\u0434\u0435 \u043f\u0456\u0434\u0456\u0431\u0440\u0430\u0442\u0438 \u043c\u043e\u0434\u0435\u043b\u044c \u043f\u043e\u043b\u0456\u043d\u043e\u043c\u0456\u0430\u043b\u044c\u043d\u043e\u0457 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457 \u0434\u043e \u0434\u0430\u043d\u0438\u0445, \u0449\u043e\u0431 \u043e\u0445\u043e\u043f\u0438\u0442\u0438 \u043d\u0435\u043b\u0456\u043d\u0456\u0439\u043d\u0438\u0439 \u0437\u0432\u2019\u044f\u0437\u043e\u043a \u043c\u0456\u0436 \u0434\u0432\u043e\u043c\u0430 \u0437\u043c\u0456\u043d\u043d\u0438\u043c\u0438.<\/span><\/p>\n
 \u041a\u0440\u043e\u043a 2. \u041f\u0456\u0434\u0431\u0435\u0440\u0456\u0442\u044c \u043c\u043e\u0434\u0435\u043b\u044c \u043f\u043e\u043b\u0456\u043d\u043e\u043c\u0456\u0430\u043b\u044c\u043d\u043e\u0457 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457<\/strong><\/span><\/h2>\n
 \u0423 \u043d\u0430\u0432\u0435\u0434\u0435\u043d\u043e\u043c\u0443 \u043d\u0438\u0436\u0447\u0435 \u043a\u043e\u0434\u0456 \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u043e, \u044f\u043a \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0456\u0457 sklearn \u0434\u043b\u044f \u043f\u0456\u0434\u0433\u043e\u043d\u043a\u0438 \u043c\u043e\u0434\u0435\u043b\u0456 \u043f\u043e\u043b\u0456\u043d\u043e\u043c\u0456\u0430\u043b\u044c\u043d\u043e\u0457 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457 \u0442\u0440\u0435\u0442\u044c\u043e\u0433\u043e \u0441\u0442\u0443\u043f\u0435\u043d\u044f \u0434\u043e \u0446\u044c\u043e\u0433\u043e \u043d\u0430\u0431\u043e\u0440\u0443 \u0434\u0430\u043d\u0438\u0445:<\/span><\/p>\n
 from<\/span> sklearn. preprocessing<\/span> import<\/span> PolynomialFeatures\nfrom<\/span> sklearn. linear_model<\/span> import<\/span> LinearRegression\n\n#specify degree of 3 for polynomial regression model\n#include bias=False means don't force y-intercept to equal zero<\/span>\npoly = PolynomialFeatures(degree= 3<\/span> , include_bias= False<\/span> )\n\n#reshape data to work properly with sklearn\n<\/span>poly_features = poly. fit_transform<\/span> ( x.reshape<\/span> (-1, 1))\n\n#fit polynomial regression model\n<\/span>poly_reg_model = LinearRegression()\npoly_reg_model. fit<\/span> (poly_features,y)\n\n#display model coefficients\n<\/span>print<\/span> (poly_reg_model. intercept_<\/span> , poly_reg_model. coef_<\/span> )\n\n33.62640037532282 [-11.83877127 2.25592957 -0.10889554]\n<\/strong><\/span><\/pre>\n
 \u0412\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u044e\u0447\u0438 \u043a\u043e\u0435\u0444\u0456\u0446\u0456\u0454\u043d\u0442\u0438 \u043c\u043e\u0434\u0435\u043b\u0456, \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u0456 \u0432 \u043e\u0441\u0442\u0430\u043d\u043d\u044c\u043e\u043c\u0443 \u0440\u044f\u0434\u043a\u0443, \u043c\u0438 \u043c\u043e\u0436\u0435\u043c\u043e \u0437\u0430\u043f\u0438\u0441\u0430\u0442\u0438 \u043f\u0456\u0434\u0456\u0431\u0440\u0430\u043d\u0435 \u0440\u0456\u0432\u043d\u044f\u043d\u043d\u044f \u043f\u043e\u043b\u0456\u043d\u043e\u043c\u0456\u0430\u043b\u044c\u043d\u043e\u0457 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457 \u0442\u0430\u043a\u0438\u043c \u0447\u0438\u043d\u043e\u043c:<\/span><\/p>\n
 y = -0,109x 3<\/sup> + 2,256x 2<\/sup> \u2013 11,839x + 33,626<\/span><\/p>\n
 \u0426\u0435 \u0440\u0456\u0432\u043d\u044f\u043d\u043d\u044f \u043c\u043e\u0436\u043d\u0430 \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u0434\u043b\u044f \u0437\u043d\u0430\u0445\u043e\u0434\u0436\u0435\u043d\u043d\u044f \u043e\u0447\u0456\u043a\u0443\u0432\u0430\u043d\u043e\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u0437\u043c\u0456\u043d\u043d\u043e\u0457 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0456 \u0437\u0430 \u0434\u0430\u043d\u043e\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u043f\u0440\u043e\u0433\u043d\u043e\u0437\u043e\u0432\u0430\u043d\u043e\u0457 \u0437\u043c\u0456\u043d\u043d\u043e\u0457.<\/span><\/p>\n
 \u041d\u0430\u043f\u0440\u0438\u043a\u043b\u0430\u0434, \u044f\u043a\u0449\u043e x \u0434\u043e\u0440\u0456\u0432\u043d\u044e\u0454 4, \u043e\u0447\u0456\u043a\u0443\u0432\u0430\u043d\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u0434\u043b\u044f \u0437\u043c\u0456\u043d\u043d\u043e\u0457 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0456 y \u0431\u0443\u0434\u0435 15,39:<\/span><\/p>\n
 y = -0,109(4) 3<\/sup> + 2,256(4) 2<\/sup> \u2013 11,839(4) + 33,626= 15,39<\/span><\/p>\n
 \u041f\u0440\u0438\u043c\u0456\u0442\u043a\u0430<\/strong> . \u0429\u043e\u0431 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0430\u0442\u0438 \u043c\u043e\u0434\u0435\u043b\u0456 \u043f\u043e\u043b\u0456\u043d\u043e\u043c\u0456\u0430\u043b\u044c\u043d\u043e\u0457 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457 \u0437 \u0456\u043d\u0448\u0438\u043c \u0441\u0442\u0443\u043f\u0435\u043d\u0435\u043c, \u043f\u0440\u043e\u0441\u0442\u043e \u0437\u043c\u0456\u043d\u0456\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0443 \u0441\u0442\u0443\u043f\u0435\u043d\u044f<\/strong> \u0443 \u0444\u0443\u043d\u043a\u0446\u0456\u0457 PolynomialFeatures()<\/strong> .<\/span><\/p>\n
 \u041a\u0440\u043e\u043a 3: \u0412\u0456\u0437\u0443\u0430\u043b\u0456\u0437\u0443\u0439\u0442\u0435 \u043c\u043e\u0434\u0435\u043b\u044c \u043f\u043e\u043b\u0456\u043d\u043e\u043c\u0456\u0430\u043b\u044c\u043d\u043e\u0457 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457<\/span><\/strong><\/h2>\n
 \u041d\u0430\u0440\u0435\u0448\u0442\u0456, \u043c\u0438 \u043c\u043e\u0436\u0435\u043c\u043e \u0441\u0442\u0432\u043e\u0440\u0438\u0442\u0438 \u043f\u0440\u043e\u0441\u0442\u0438\u0439 \u0433\u0440\u0430\u0444\u0456\u043a \u0434\u043b\u044f \u0432\u0456\u0437\u0443\u0430\u043b\u0456\u0437\u0430\u0446\u0456\u0457 \u043c\u043e\u0434\u0435\u043b\u0456 \u043f\u043e\u043b\u0456\u043d\u043e\u043c\u0456\u0430\u043b\u044c\u043d\u043e\u0457 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457, \u043f\u0456\u0434\u0456\u0433\u043d\u0430\u043d\u043e\u0457 \u0434\u043e \u0432\u0438\u0445\u0456\u0434\u043d\u0438\u0445 \u0442\u043e\u0447\u043e\u043a \u0434\u0430\u043d\u0438\u0445:<\/span><\/span> <\/p>\n
 #use model to make predictions on response variable\n<\/span>y_predicted = poly_reg_model. predict<\/span> (poly_features)\n\n#create scatterplot of x vs. y\n<\/span>plt. scatter<\/span> (x,y)\n\n#add line to show fitted polynomial regression model\n<\/span>plt. plot<\/span> (x,y_predicted,color=' purple<\/span> ')\n<\/strong><\/span><\/pre>\n
\"\"<\/p>\n
 \u041f\u0440\u0438\u043c\u0456\u0442\u043a\u0430<\/strong> . \u0412\u0438 \u043c\u043e\u0436\u0435\u0442\u0435 \u0437\u043d\u0430\u0439\u0442\u0438 \u043f\u043e\u0432\u043d\u0443 \u0434\u043e\u043a\u0443\u043c\u0435\u043d\u0442\u0430\u0446\u0456\u044e \u0434\u043b\u044f \u0444\u0443\u043d\u043a\u0446\u0456\u0457 sklearn PolynomialFeatures()<\/strong> \u0442\u0443\u0442<\/a> .<\/span><\/p>\n
 \u0414\u043e\u0434\u0430\u0442\u043a\u043e\u0432\u0456 \u0440\u0435\u0441\u0443\u0440\u0441\u0438<\/span><\/strong><\/span><\/h2>\n
 \u0423 \u043d\u0430\u0441\u0442\u0443\u043f\u043d\u0438\u0445 \u043f\u043e\u0441\u0456\u0431\u043d\u0438\u043a\u0430\u0445 \u043f\u043e\u044f\u0441\u043d\u044e\u0454\u0442\u044c\u0441\u044f, \u044f\u043a \u0432\u0438\u043a\u043e\u043d\u0443\u0432\u0430\u0442\u0438 \u0456\u043d\u0448\u0456 \u0442\u0438\u043f\u043e\u0432\u0456 \u0437\u0430\u0432\u0434\u0430\u043d\u043d\u044f \u0437\u0430 \u0434\u043e\u043f\u043e\u043c\u043e\u0433\u043e\u044e sklearn:<\/span><\/p>\n
 \u042f\u043a \u043e\u0442\u0440\u0438\u043c\u0430\u0442\u0438 \u043a\u043e\u0435\u0444\u0456\u0446\u0456\u0454\u043d\u0442\u0438 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457 \u0437 sklearn<\/a>
 \u042f\u043a \u0440\u043e\u0437\u0440\u0430\u0445\u0443\u0432\u0430\u0442\u0438 \u0437\u0431\u0430\u043b\u0430\u043d\u0441\u043e\u0432\u0430\u043d\u0443 \u0442\u043e\u0447\u043d\u0456\u0441\u0442\u044c \u0437\u0430 \u0434\u043e\u043f\u043e\u043c\u043e\u0433\u043e\u044e sklearn<\/a>
 \u042f\u043a \u0456\u043d\u0442\u0435\u0440\u043f\u0440\u0435\u0442\u0443\u0432\u0430\u0442\u0438 \u043a\u043b\u0430\u0441\u0438\u0444\u0456\u043a\u0430\u0446\u0456\u0439\u043d\u0438\u0439 \u0437\u0432\u0456\u0442 \u0443 Sklearn<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
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\u043f\u043e\u043b\u0456\u043d\u043e\u043c\u0430. \u041d\u0430\u0441\u0442\u0443\u043f\u043d\u0438\u0439 \u043f\u043e\u043a\u0440\u043e\u043a\u043e\u0432\u0438\u0439 \u043f\u0440\u0438\u043a\u043b\u0430\u0434 \u043f\u043e\u043a\u0430\u0437\u0443\u0454, \u044f\u043a \u0432\u0438\u043a\u043e\u043d\u0430\u0442\u0438 \u043f\u043e\u043b\u0456\u043d\u043e\u043c\u0456\u0430\u043b\u044c\u043d\u0443 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u044e \u0432 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"yoast_head":"\n\u042f\u043a \u0432\u0438\u043a\u043e\u043d\u0430\u0442\u0438 \u043f\u043e\u043b\u0456\u043d\u043e\u043c\u0456\u0430\u043b\u044c\u043d\u0443 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u044e \u0437\u0430 \u0434\u043e\u043f\u043e\u043c\u043e\u0433\u043e\u044e Scikit-Learn - 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