{"id":1203,"date":"2023-07-27T07:20:18","date_gmt":"2023-07-27T07:20:18","guid":{"rendered":"https:\/\/statorials.org\/ru\/%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81%d1%81%d0%b8%d1%8f-%d0%be%d1%81%d0%bd%d0%be%d0%b2%d0%bd%d1%8b%d1%85-%d0%ba%d0%be%d0%bc%d0%bf%d0%be%d0%bd%d0%b5%d0%bd%d1%82%d0%be%d0%b2-%d0%b2-python\/"},"modified":"2023-07-27T07:20:18","modified_gmt":"2023-07-27T07:20:18","slug":"%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81%d1%81%d0%b8%d1%8f-%d0%be%d1%81%d0%bd%d0%be%d0%b2%d0%bd%d1%8b%d1%85-%d0%ba%d0%be%d0%bc%d0%bf%d0%be%d0%bd%d0%b5%d0%bd%d1%82%d0%be%d0%b2-%d0%b2-python","status":"publish","type":"post","link":"https:\/\/statorials.org\/ru\/%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81%d1%81%d0%b8%d1%8f-%d0%be%d1%81%d0%bd%d0%be%d0%b2%d0%bd%d1%8b%d1%85-%d0%ba%d0%be%d0%bc%d0%bf%d0%be%d0%bd%d0%b5%d0%bd%d1%82%d0%be%d0%b2-%d0%b2-python\/","title":{"rendered":"\u0420\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f \u0433\u043b\u0430\u0432\u043d\u044b\u0445 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u043e\u0432 \u0432 python (\u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0423\u0447\u0438\u0442\u044b\u0432\u0430\u044f \u043d\u0430\u0431\u043e\u0440 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445-\u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u043e\u0432 <em>p<\/em> \u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0443\u044e \u043e\u0442\u043a\u043b\u0438\u043a\u0430, <a href=\"https:\/\/statorials.org\/ru\/\u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f-\u043b\u0438\u043d\u0435\u0438\u043d\u0430\u044f-\u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f<\/a> \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442 \u043c\u0435\u0442\u043e\u0434, \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0439 \u043a\u0430\u043a \u043d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0438\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u044b, \u0434\u043b\u044f \u043c\u0438\u043d\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e\u0439 \u0441\u0443\u043c\u043c\u044b \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432 (RSS):<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>RSS = \u03a3(y <sub>i<\/sub> \u2013 \u0177 <sub>i<\/sub> ) <sup>2<\/sup><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0417\u043e\u043b\u043e\u0442\u043e:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> : \u0433\u0440\u0435\u0447\u0435\u0441\u043a\u0438\u0439 \u0441\u0438\u043c\u0432\u043e\u043b, \u043e\u0437\u043d\u0430\u0447\u0430\u044e\u0449\u0438\u0439 <em>\u0441\u0443\u043c\u043c\u0443.<\/em><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>y <sub>i<\/sub><\/strong> : \u0444\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043e\u0442\u0432\u0435\u0442\u0430 \u0434\u043b\u044f <sup>i-\u0433\u043e<\/sup> \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u044f<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u0177 <sub>i<\/sub><\/strong> : \u043f\u0440\u043e\u0433\u043d\u043e\u0437\u0438\u0440\u0443\u0435\u043c\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043e\u0442\u0432\u0435\u0442\u0430 \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 \u043c\u043e\u0434\u0435\u043b\u0438 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0439 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u041e\u0434\u043d\u0430\u043a\u043e, \u043a\u043e\u0433\u0434\u0430 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0435-\u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u044b \u0441\u0438\u043b\u044c\u043d\u043e \u043a\u043e\u0440\u0440\u0435\u043b\u0438\u0440\u0443\u044e\u0442,<\/span> <a href=\"https:\/\/statorials.org\/ru\/\u043c\u0443\u043b\u044c\u0442\u0438\u043a\u043e\u043b\u043b\u0438\u043d\u0435\u0430\u0440\u043d\u0430\u044f-\u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u043c\u0443\u043b\u044c\u0442\u0438\u043a\u043e\u043b\u043b\u0438\u043d\u0435\u0430\u0440\u043d\u043e\u0441\u0442\u044c<\/a> <span style=\"color: #000000;\">\u043c\u043e\u0436\u0435\u0442 \u0441\u0442\u0430\u0442\u044c \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u043e\u0439. \u042d\u0442\u043e \u043c\u043e\u0436\u0435\u0442 \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u043e\u0446\u0435\u043d\u043a\u0438 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u0432 \u043c\u043e\u0434\u0435\u043b\u0438 \u043d\u0435\u043d\u0430\u0434\u0435\u0436\u043d\u044b\u043c\u0438 \u0438 \u043f\u0440\u0438\u0432\u0435\u0441\u0442\u0438 \u043a \u0432\u044b\u0441\u043e\u043a\u043e\u0439 \u0434\u0438\u0441\u043f\u0435\u0440\u0441\u0438\u0438.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u041e\u0434\u0438\u043d \u0438\u0437 \u0441\u043f\u043e\u0441\u043e\u0431\u043e\u0432 \u0438\u0437\u0431\u0435\u0436\u0430\u0442\u044c \u044d\u0442\u043e\u0439 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u2014 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c <a href=\"https:\/\/statorials.org\/ru\/\u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f-\u0433\u043b\u0430\u0432\u043d\u044b\u0445-\u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044e \u0433\u043b\u0430\u0432\u043d\u044b\u0445 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u043e\u0432<\/a> , \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043d\u0430\u0445\u043e\u0434\u0438\u0442 <em>M<\/em> \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0445 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0439 (\u043d\u0430\u0437\u044b\u0432\u0430\u0435\u043c\u044b\u0445 \u00ab\u0433\u043b\u0430\u0432\u043d\u044b\u043c\u0438 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0430\u043c\u0438\u00bb) \u0438\u0441\u0445\u043e\u0434\u043d\u044b\u0445 <em>p-<\/em> \u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u043e\u0432, \u0430 \u0437\u0430\u0442\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442 \u043c\u0435\u0442\u043e\u0434 \u043d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0438\u0445 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432 \u0434\u043b\u044f \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0438\u044f \u043c\u043e\u0434\u0435\u043b\u0438 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0433\u043b\u0430\u0432\u043d\u044b\u0435 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u0432 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u043e\u0432.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0412 \u044d\u0442\u043e\u043c \u0440\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0439 \u043f\u0440\u0438\u043c\u0435\u0440 \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u0438\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u0433\u043b\u0430\u0432\u043d\u044b\u0445 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u043e\u0432 \u0432 Python.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u0428\u0430\u0433&nbsp;1. \u0418\u043c\u043f\u043e\u0440\u0442\u0438\u0440\u0443\u0439\u0442\u0435 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u044b\u0435 \u043f\u0430\u043a\u0435\u0442\u044b.<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">\u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u043c\u044b \u0438\u043c\u043f\u043e\u0440\u0442\u0438\u0440\u0443\u0435\u043c \u043f\u0430\u043a\u0435\u0442\u044b, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u044b\u0435 \u0434\u043b\u044f \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u0438\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u0433\u043b\u0430\u0432\u043d\u044b\u0445 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u043e\u0432 (PCR) \u0432 Python:<\/span><\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n<span style=\"color: #008000;\">import<\/span> pandas <span style=\"color: #008000;\">as<\/span> pd\n<span style=\"color: #008000;\">import<\/span> matplotlib. <span style=\"color: #3366ff;\">pyplot<\/span> <span style=\"color: #008000;\">as<\/span> plt\n<span style=\"color: #008000;\">from<\/span> sklearn. <span style=\"color: #3366ff;\">preprocessing<\/span> <span style=\"color: #008000;\">import<\/span> scale \n<span style=\"color: #008000;\">from<\/span> sklearn <span style=\"color: #008000;\">import<\/span> model_selection\n<span style=\"color: #008000;\">from<\/span> sklearn. <span style=\"color: #3366ff;\">model_selection<\/span> <span style=\"color: #008000;\">import<\/span> RepeatedKFold\n<span style=\"color: #008000;\">from<\/span> sklearn.model_selection <span style=\"color: #008000;\">import<\/span> train_test_split\n<span style=\"color: #008000;\">from<\/span> sklearn. PCA <span style=\"color: #008000;\">import<\/span> <span style=\"color: #3366ff;\">decomposition<\/span>\n<span style=\"color: #008000;\">from<\/span> sklearn. <span style=\"color: #3366ff;\">linear_model<\/span> <span style=\"color: #008000;\">import<\/span> LinearRegression\n<span style=\"color: #008000;\">from<\/span> sklearn. <span style=\"color: #3366ff;\">metrics<\/span> <span style=\"color: #008000;\">import<\/span> mean_squared_error\n<\/strong><\/span><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>\u0428\u0430\u0433 2. \u0417\u0430\u0433\u0440\u0443\u0437\u0438\u0442\u0435 \u0434\u0430\u043d\u043d\u044b\u0435<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0412 \u044d\u0442\u043e\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043d\u0430\u0431\u043e\u0440 \u0434\u0430\u043d\u043d\u044b\u0445 <strong>mtcars<\/strong> , \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0441\u043e\u0434\u0435\u0440\u0436\u0438\u0442 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u044e \u043e 33 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0445 \u0430\u0432\u0442\u043e\u043c\u043e\u0431\u0438\u043b\u044f\u0445. \u041c\u044b \u0431\u0443\u0434\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c <strong>hp<\/strong> \u0432 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u043e\u0442\u0432\u0435\u0442\u0430 \u0438 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0435 \u0432 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u043e\u0432:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u043c\u0438\u043b\u044c \u043d\u0430 \u0433\u0430\u043b\u043b\u043e\u043d<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u043e\u0442\u043e\u0431\u0440\u0430\u0436\u0430\u0442\u044c<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0434\u0435\u0440\u044c\u043c\u043e<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u043c\u0430\u0441\u0441\u0430<\/span><\/li>\n<li> <span style=\"color: #000000;\">qsec<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">\u0421\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u043a\u043e\u0434 \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442, \u043a\u0430\u043a \u0437\u0430\u0433\u0440\u0443\u0437\u0438\u0442\u044c \u0438 \u043e\u0442\u043e\u0431\u0440\u0430\u0437\u0438\u0442\u044c \u044d\u0442\u043e\u0442 \u043d\u0430\u0431\u043e\u0440 \u0434\u0430\u043d\u043d\u044b\u0445:<\/span><\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#define URL where data is located\n<\/span>url = \"https:\/\/raw.githubusercontent.com\/Statorials\/Python-Guides\/main\/mtcars.csv\"\n\n<span style=\"color: #008080;\">#read in data\n<\/span>data_full = pd. <span style=\"color: #3366ff;\">read_csv<\/span> (url)\n\n<span style=\"color: #008080;\">#select subset of data\n<\/span>data = data_full[[\"mpg\", \"disp\", \"drat\", \"wt\", \"qsec\", \"hp\"]]\n\n<span style=\"color: #008080;\">#view first six rows of data\n<\/span>data[0:6]\n\n\n        mpg disp drat wt qsec hp\n0 21.0 160.0 3.90 2.620 16.46 110\n1 21.0 160.0 3.90 2.875 17.02 110\n2 22.8 108.0 3.85 2.320 18.61 93\n3 21.4 258.0 3.08 3.215 19.44 110\n4 18.7 360.0 3.15 3.440 17.02 175\n5 18.1 225.0 2.76 3.460 20.22 105<\/strong><\/span><\/pre>\n<h3> <strong>\u0428\u0430\u0433 3. \u041d\u0430\u0441\u0442\u0440\u043e\u0439\u0442\u0435 \u043c\u043e\u0434\u0435\u043b\u044c \u041f\u0426\u0420<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">\u0421\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u043a\u043e\u0434 \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442, \u043a\u0430\u043a \u043f\u043e\u0434\u043e\u0433\u043d\u0430\u0442\u044c \u043c\u043e\u0434\u0435\u043b\u044c PCR \u043a \u044d\u0442\u0438\u043c \u0434\u0430\u043d\u043d\u044b\u043c. \u041e\u0431\u0440\u0430\u0442\u0438\u0442\u0435 \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435 \u043d\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>pca.fit_transform(scale(X))<\/strong> : \u044d\u0442\u043e \u0441\u043e\u043e\u0431\u0449\u0430\u0435\u0442 Python, \u0447\u0442\u043e \u043a\u0430\u0436\u0434\u0430\u044f \u0438\u0437 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445-\u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u043e\u0432 \u0434\u043e\u043b\u0436\u043d\u0430 \u0431\u044b\u0442\u044c \u043c\u0430\u0441\u0448\u0442\u0430\u0431\u0438\u0440\u043e\u0432\u0430\u043d\u0430 \u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b \u0438\u043c\u0435\u0442\u044c \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 0 \u0438 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0435 \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u0435 1. \u042d\u0442\u043e \u0433\u0430\u0440\u0430\u043d\u0442\u0438\u0440\u0443\u0435\u0442, \u0447\u0442\u043e \u043d\u0438 \u043e\u0434\u043d\u0430 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0430\u044f-\u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440 \u043d\u0435 \u0431\u0443\u0434\u0435\u0442 \u0438\u043c\u0435\u0442\u044c \u0441\u043b\u0438\u0448\u043a\u043e\u043c \u0431\u043e\u043b\u044c\u0448\u043e\u0433\u043e \u0432\u043b\u0438\u044f\u043d\u0438\u044f \u043d\u0430 \u043c\u043e\u0434\u0435\u043b\u044c, \u0435\u0441\u043b\u0438 \u044d\u0442\u043e \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442. \u0438\u0437\u043c\u0435\u0440\u044f\u0442\u044c \u0432 \u0440\u0430\u0437\u043d\u044b\u0445 \u0435\u0434\u0438\u043d\u0438\u0446\u0430\u0445.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>cv = RepeatedKFold()<\/strong> : \u044d\u0442\u043e \u0433\u043e\u0432\u043e\u0440\u0438\u0442 Python \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c <a href=\"https:\/\/statorials.org\/ru\/k-\u043a\u0440\u0430\u0442\u043d\u0430\u044f-\u043f\u0435\u0440\u0435\u043a\u0440\u0435\u0441\u0442\u043d\u0430\u044f-\u043f\u0440\u043e\u0432\u0435\u0440\u043a\u0430\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u043f\u0435\u0440\u0435\u043a\u0440\u0435\u0441\u0442\u043d\u0443\u044e \u043f\u0440\u043e\u0432\u0435\u0440\u043a\u0443 \u0432 k-\u043a\u0440\u0430\u0442\u043d\u043e\u043c \u0440\u0430\u0437\u043c\u0435\u0440\u0435<\/a> \u0434\u043b\u044f \u043e\u0446\u0435\u043d\u043a\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u0438 \u043c\u043e\u0434\u0435\u043b\u0438. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u0430 \u043c\u044b \u0432\u044b\u0431\u0438\u0440\u0430\u0435\u043c k = 10 \u0441\u043a\u043b\u0430\u0434\u043e\u043a, \u043f\u043e\u0432\u0442\u043e\u0440\u044f\u0435\u043c 3 \u0440\u0430\u0437\u0430.<\/span> <\/li>\n<\/ul>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#define predictor and response variables\n<\/span>X = data[[\"mpg\", \"disp\", \"drat\", \"wt\", \"qsec\"]]\ny = data[[\"hp\"]]\n\n<span style=\"color: #008080;\">#scale predictor variables\n<\/span>pca = pca()\nX_reduced = pca. <span style=\"color: #3366ff;\">fit_transform<\/span> ( <span style=\"color: #3366ff;\">scale<\/span> (X))\n\n<span style=\"color: #008080;\">#define cross validation method\n<\/span>cv = RepeatedKFold(n_splits= <span style=\"color: #008000;\">10<\/span> , n_repeats= <span style=\"color: #008000;\">3<\/span> , random_state= <span style=\"color: #008000;\">1<\/span> )\n\nregr = LinearRegression()\nmse = []\n\n<span style=\"color: #008080;\"># Calculate MSE with only the intercept\n<\/span>score = -1*model_selection. <span style=\"color: #3366ff;\">cross_val_score<\/span> (regr,\n           n.p. <span style=\"color: #3366ff;\">ones<\/span> ((len(X_reduced),1)), y, cv=cv,\n           scoring=' <span style=\"color: #008000;\">neg_mean_squared_error<\/span> '). <span style=\"color: #3366ff;\">mean<\/span> ()    \nmse. <span style=\"color: #3366ff;\">append<\/span> (score)\n\n<span style=\"color: #008080;\"># Calculate MSE using cross-validation, adding one component at a time\n<\/span><span style=\"color: #008000;\">for<\/span> i <span style=\"color: #008000;\">in<\/span> np. <span style=\"color: #3366ff;\">arange<\/span> (1, 6):\n    score = -1*model_selection. <span style=\"color: #3366ff;\">cross_val_score<\/span> (regr,\n               X_reduced[:,:i], y, cv=cv, scoring=' <span style=\"color: #008000;\">neg_mean_squared_error<\/span> '). <span style=\"color: #3366ff;\">mean<\/span> ()\n    mse. <span style=\"color: #3366ff;\">append<\/span> (score)\n    \n<span style=\"color: #008080;\"># Plot cross-validation results    \n<\/span>plt. <span style=\"color: #3366ff;\">plot<\/span> (mse)\nplt. <span style=\"color: #3366ff;\">xlabel<\/span> ('Number of Principal Components')\nplt. <span style=\"color: #3366ff;\">ylabel<\/span> ('MSE')\nplt. <span style=\"color: #3366ff;\">title<\/span> ('hp')<\/strong><\/span> <\/pre>\n<h3><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11950 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/pcrpython1.png\" alt=\"\u0420\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f \u0433\u043b\u0430\u0432\u043d\u044b\u0445 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u043e\u0432 \u0432 Python\" width=\"424\" height=\"285\" srcset=\"\" sizes=\"auto, \"><\/h3>\n<p> <span style=\"color: #000000;\">\u041d\u0430 \u0433\u0440\u0430\u0444\u0438\u043a\u0435 \u043e\u0442\u043e\u0431\u0440\u0430\u0436\u0430\u0435\u0442\u0441\u044f \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0433\u043b\u0430\u0432\u043d\u044b\u0445 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u043e\u0432 \u043f\u043e \u043e\u0441\u0438 X \u0438 \u0442\u0435\u0441\u0442 MSE (\u0441\u0440\u0435\u0434\u043d\u0435\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u043e\u0448\u0438\u0431\u043a\u0430) \u043f\u043e \u043e\u0441\u0438 Y.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u041d\u0430 \u0433\u0440\u0430\u0444\u0438\u043a\u0435 \u043c\u044b \u0432\u0438\u0434\u0438\u043c, \u0447\u0442\u043e MSE \u0442\u0435\u0441\u0442\u0430 \u0443\u043c\u0435\u043d\u044c\u0448\u0430\u0435\u0442\u0441\u044f \u043f\u0440\u0438 \u0434\u043e\u0431\u0430\u0432\u043b\u0435\u043d\u0438\u0438 \u0434\u0432\u0443\u0445 \u0433\u043b\u0430\u0432\u043d\u044b\u0445 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u043e\u0432, \u043d\u043e \u043d\u0430\u0447\u0438\u043d\u0430\u0435\u0442 \u0443\u0432\u0435\u043b\u0438\u0447\u0438\u0432\u0430\u0442\u044c\u0441\u044f, \u043a\u043e\u0433\u0434\u0430 \u043c\u044b \u0434\u043e\u0431\u0430\u0432\u043b\u044f\u0435\u043c \u0431\u043e\u043b\u0435\u0435 \u0434\u0432\u0443\u0445 \u0433\u043b\u0430\u0432\u043d\u044b\u0445 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u043e\u0432.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043e\u043f\u0442\u0438\u043c\u0430\u043b\u044c\u043d\u0430\u044f \u043c\u043e\u0434\u0435\u043b\u044c \u0432\u043a\u043b\u044e\u0447\u0430\u0435\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u0435\u0440\u0432\u044b\u0435 \u0434\u0432\u0435 \u0433\u043b\u0430\u0432\u043d\u044b\u0435 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u041c\u044b \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u043a\u043e\u0434 \u0434\u043b\u044f \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u043f\u0440\u043e\u0446\u0435\u043d\u0442\u0430 \u0434\u0438\u0441\u043f\u0435\u0440\u0441\u0438\u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u043e\u0442\u0432\u0435\u0442\u0430, \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u043c\u043e\u0439 \u043f\u0443\u0442\u0435\u043c \u0434\u043e\u0431\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u043e\u0441\u043d\u043e\u0432\u043d\u043e\u0433\u043e \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0430 \u0432 \u043c\u043e\u0434\u0435\u043b\u044c:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong>n.p. <span style=\"color: #3366ff;\">cumsum<\/span> (np. <span style=\"color: #3366ff;\">round<\/span> (pca. <span style=\"color: #3366ff;\">explained_variance_ratio_<\/span> , decimals= <span style=\"color: #008000;\">4<\/span> )* <span style=\"color: #008000;\">100<\/span> )\n\narray([69.83, 89.35, 95.88, 98.95, 99.99])\n<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">\u041c\u044b \u043c\u043e\u0436\u0435\u043c \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u0418\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u0435\u0440\u0432\u044b\u0439 \u0433\u043b\u0430\u0432\u043d\u044b\u0439 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u0442\u044c <strong>69,83%<\/strong> \u0432\u0430\u0440\u0438\u0430\u0446\u0438\u0439 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u043e\u0442\u043a\u043b\u0438\u043a\u0430.<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0414\u043e\u0431\u0430\u0432\u043b\u044f\u044f \u0432\u0442\u043e\u0440\u043e\u0439 \u0433\u043b\u0430\u0432\u043d\u044b\u0439 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u0442\u044c <strong>89,35%<\/strong> \u0432\u0430\u0440\u0438\u0430\u0446\u0438\u0439 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u043e\u0442\u043a\u043b\u0438\u043a\u0430.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u041e\u0431\u0440\u0430\u0442\u0438\u0442\u0435 \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435, \u0447\u0442\u043e \u043c\u044b \u043f\u043e-\u043f\u0440\u0435\u0436\u043d\u0435\u043c\u0443 \u0441\u043c\u043e\u0436\u0435\u043c \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u0442\u044c \u0431\u043e\u043b\u044c\u0448\u0443\u044e \u0434\u0438\u0441\u043f\u0435\u0440\u0441\u0438\u044e, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0431\u043e\u043b\u044c\u0448\u0435 \u0433\u043b\u0430\u0432\u043d\u044b\u0445 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u043e\u0432, \u043d\u043e \u043c\u044b \u0432\u0438\u0434\u0438\u043c, \u0447\u0442\u043e \u0434\u043e\u0431\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0431\u043e\u043b\u0435\u0435 \u0434\u0432\u0443\u0445 \u0433\u043b\u0430\u0432\u043d\u044b\u0445 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u043e\u0432 \u043d\u0430 \u0441\u0430\u043c\u043e\u043c \u0434\u0435\u043b\u0435 \u043d\u0435 \u0441\u0438\u043b\u044c\u043d\u043e \u0443\u0432\u0435\u043b\u0438\u0447\u0438\u0432\u0430\u0435\u0442 \u043f\u0440\u043e\u0446\u0435\u043d\u0442 \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u043d\u043e\u0439 \u0434\u0438\u0441\u043f\u0435\u0440\u0441\u0438\u0438.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u0428\u0430\u0433 4. \u0418\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0439\u0442\u0435 \u043e\u043a\u043e\u043d\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u0443\u044e \u043c\u043e\u0434\u0435\u043b\u044c \u0434\u043b\u044f \u043f\u0440\u043e\u0433\u043d\u043e\u0437\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u041c\u044b \u043c\u043e\u0436\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043e\u043a\u043e\u043d\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u0443\u044e \u0434\u0432\u0443\u0445\u0433\u043b\u0430\u0432\u043d\u0443\u044e \u043c\u043e\u0434\u0435\u043b\u044c \u041f\u0426\u0420 \u0434\u043b\u044f \u043f\u0440\u043e\u0433\u043d\u043e\u0437\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u043d\u043e\u0432\u044b\u0445 \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u0439.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0421\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u043a\u043e\u0434 \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442, \u043a\u0430\u043a \u0440\u0430\u0437\u0434\u0435\u043b\u0438\u0442\u044c \u0438\u0441\u0445\u043e\u0434\u043d\u044b\u0439 \u043d\u0430\u0431\u043e\u0440 \u0434\u0430\u043d\u043d\u044b\u0445 \u043d\u0430 \u043e\u0431\u0443\u0447\u0430\u044e\u0449\u0438\u0439 \u0438 \u0442\u0435\u0441\u0442\u043e\u0432\u044b\u0439 \u043d\u0430\u0431\u043e\u0440 \u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043c\u043e\u0434\u0435\u043b\u044c PCR \u0441 \u0434\u0432\u0443\u043c\u044f \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u043c\u0438 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0430\u043c\u0438 \u0434\u043b\u044f \u043f\u0440\u043e\u0433\u043d\u043e\u0437\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u0442\u0435\u0441\u0442\u043e\u0432\u043e\u0433\u043e \u043d\u0430\u0431\u043e\u0440\u0430.<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#split the dataset into training (70%) and testing (30%) sets\n<\/span>X_train,X_test,y_train,y_test = <span style=\"color: #3366ff;\">train_test_split<\/span> (X,y,test_size= <span style=\"color: #008000;\">0.3<\/span> , random_state= <span style=\"color: #008000;\">0<\/span> ) \n\n<span style=\"color: #008080;\">#scale the training and testing data\n<\/span>X_reduced_train = pca. <span style=\"color: #3366ff;\">fit_transform<\/span> ( <span style=\"color: #3366ff;\">scale<\/span> (X_train))\nX_reduced_test = pca. <span style=\"color: #3366ff;\">transform<\/span> ( <span style=\"color: #3366ff;\">scale<\/span> (X_test))[:,:1]\n\n<span style=\"color: #008080;\">#train PCR model on training data \n<\/span>regr = LinearRegression()\nreg. <span style=\"color: #3366ff;\">fit<\/span> (X_reduced_train[:,:1], y_train)\n\n<span style=\"color: #008080;\">#calculate RMSE\n<\/span>pred = regr. <span style=\"color: #3366ff;\">predict<\/span> (X_reduced_test)\nn.p. <span style=\"color: #3366ff;\">sqrt<\/span> ( <span style=\"color: #3366ff;\">mean_squared_error<\/span> (y_test, pred))\n\n40.2096\n<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">\u041c\u044b \u0432\u0438\u0434\u0438\u043c, \u0447\u0442\u043e \u0442\u0435\u0441\u0442 RMSE \u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0440\u0430\u0432\u043d\u044b\u043c <strong>40.2096<\/strong> . \u042d\u0442\u043e \u0441\u0440\u0435\u0434\u043d\u0435\u0435 \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u043f\u0440\u043e\u0433\u043d\u043e\u0437\u0438\u0440\u0443\u0435\u043c\u044b\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435\u043c <em>hp<\/em> \u0438 \u043d\u0430\u0431\u043b\u044e\u0434\u0430\u0435\u043c\u044b\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435\u043c <em>hp<\/em> \u0434\u043b\u044f \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u0439 \u0442\u0435\u0441\u0442\u043e\u0432\u043e\u0433\u043e \u043d\u0430\u0431\u043e\u0440\u0430.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u041f\u043e\u043b\u043d\u044b\u0439 \u043a\u043e\u0434 Python, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u043d\u044b\u0439 \u0432 \u044d\u0442\u043e\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0435, \u043c\u043e\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438 <a href=\"https:\/\/github.com\/Statorials\/Python-Guides\/blob\/main\/principal_components_regression.py\" target=\"_blank\" rel=\"noopener noreferrer\">\u0437\u0434\u0435\u0441\u044c<\/a> .<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0423\u0447\u0438\u0442\u044b\u0432\u0430\u044f \u043d\u0430\u0431\u043e\u0440 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445-\u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u043e\u0432 p \u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0443\u044e \u043e\u0442\u043a\u043b\u0438\u043a\u0430, \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442 \u043c\u0435\u0442\u043e\u0434, \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0439 \u043a\u0430\u043a \u043d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0438\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u044b, \u0434\u043b\u044f \u043c\u0438\u043d\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e\u0439 \u0441\u0443\u043c\u043c\u044b \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432 (RSS): RSS = \u03a3(y i \u2013 \u0177 i ) 2 \u0417\u043e\u043b\u043e\u0442\u043e: \u03a3 : \u0433\u0440\u0435\u0447\u0435\u0441\u043a\u0438\u0439 \u0441\u0438\u043c\u0432\u043e\u043b, \u043e\u0437\u043d\u0430\u0447\u0430\u044e\u0449\u0438\u0439 \u0441\u0443\u043c\u043c\u0443. y i : \u0444\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043e\u0442\u0432\u0435\u0442\u0430 \u0434\u043b\u044f i-\u0433\u043e \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u044f \u0177 i : \u043f\u0440\u043e\u0433\u043d\u043e\u0437\u0438\u0440\u0443\u0435\u043c\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043e\u0442\u0432\u0435\u0442\u0430 \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-1203","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0420\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f \u0433\u043b\u0430\u0432\u043d\u044b\u0445 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u043e\u0432 \u0432 Python (\u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c)<\/title>\n<meta name=\"description\" content=\"\u0412 \u044d\u0442\u043e\u043c \u0440\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u0442\u0441\u044f, \u043a\u0430\u043a \u0432\u044b\u043f\u043e\u043b\u043d\u0438\u0442\u044c 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