{"id":1207,"date":"2023-07-27T06:54:42","date_gmt":"2023-07-27T06:54:42","guid":{"rendered":"https:\/\/statorials.org\/uk\/%d0%bd%d0%b0%d0%b8%d0%bc%d0%b5%d0%bd%d1%88%d1%96-%d1%87%d0%b0%d1%81%d1%82%d0%ba%d0%be%d0%b2%d1%96-%d1%80%d0%b5%d0%b1%d1%80%d0%b0-%d0%b2-python\/"},"modified":"2023-07-27T06:54:42","modified_gmt":"2023-07-27T06:54:42","slug":"%d0%bd%d0%b0%d0%b8%d0%bc%d0%b5%d0%bd%d1%88%d1%96-%d1%87%d0%b0%d1%81%d1%82%d0%ba%d0%be%d0%b2%d1%96-%d1%80%d0%b5%d0%b1%d1%80%d0%b0-%d0%b2-python","status":"publish","type":"post","link":"https:\/\/statorials.org\/uk\/%d0%bd%d0%b0%d0%b8%d0%bc%d0%b5%d0%bd%d1%88%d1%96-%d1%87%d0%b0%d1%81%d1%82%d0%ba%d0%be%d0%b2%d1%96-%d1%80%d0%b5%d0%b1%d1%80%d0%b0-%d0%b2-python\/","title":{"rendered":"\u0427\u0430\u0441\u0442\u043a\u043e\u0432\u0456 \u043d\u0430\u0439\u043c\u0435\u043d\u0448\u0456 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438 \u0432 python (\u043a\u0440\u043e\u043a \u0437\u0430 \u043a\u0440\u043e\u043a\u043e\u043c)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u041e\u0434\u043d\u0430 \u0437 \u043d\u0430\u0439\u043f\u043e\u0448\u0438\u0440\u0435\u043d\u0456\u0448\u0438\u0445 \u043f\u0440\u043e\u0431\u043b\u0435\u043c, \u0437 \u044f\u043a\u043e\u044e \u0432\u0438 \u0437\u0456\u0442\u043a\u043d\u0435\u0442\u0435\u0441\u044f \u043f\u0456\u0434 \u0447\u0430\u0441 \u043c\u0430\u0448\u0438\u043d\u043d\u043e\u0433\u043e \u043d\u0430\u0432\u0447\u0430\u043d\u043d\u044f, \u2014 <a href=\"https:\/\/statorials.org\/uk\/\u043c\u0443\u043b\u044c\u0442\u0438\u043a\u043e\u043b\u0456\u043d\u0435\u0430\u0440\u043d\u0430-\u0440\u0435\u0433\u0440\u0435\u0441\u0456\u044f\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u043c\u0443\u043b\u044c\u0442\u0438\u043a\u043e\u043b\u0456\u043d\u0435\u0430\u0440\u043d\u0456\u0441\u0442\u044c<\/a> . \u0426\u0435 \u0432\u0456\u0434\u0431\u0443\u0432\u0430\u0454\u0442\u044c\u0441\u044f, \u043a\u043e\u043b\u0438 \u0434\u0432\u0456 \u0430\u0431\u043e \u0431\u0456\u043b\u044c\u0448\u0435 \u0437\u043c\u0456\u043d\u043d\u0438\u0445 \u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u0430 \u0432 \u043d\u0430\u0431\u043e\u0440\u0456 \u0434\u0430\u043d\u0438\u0445 \u0441\u0438\u043b\u044c\u043d\u043e \u043a\u043e\u0440\u0435\u043b\u044c\u043e\u0432\u0430\u043d\u0456.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u041a\u043e\u043b\u0438 \u0446\u0435 \u0442\u0440\u0430\u043f\u043b\u044f\u0454\u0442\u044c\u0441\u044f, \u043c\u043e\u0434\u0435\u043b\u044c \u043c\u043e\u0436\u0435 \u0434\u043e\u0431\u0440\u0435 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0430\u0442\u0438 \u043d\u0430\u0432\u0447\u0430\u043b\u044c\u043d\u043e\u043c\u0443 \u043d\u0430\u0431\u043e\u0440\u0443 \u0434\u0430\u043d\u0438\u0445, \u0430\u043b\u0435 \u043c\u043e\u0436\u0435 \u043f\u0440\u0430\u0446\u044e\u0432\u0430\u0442\u0438 \u043f\u043e\u0433\u0430\u043d\u043e \u043d\u0430 \u043d\u043e\u0432\u043e\u043c\u0443 \u043d\u0430\u0431\u043e\u0440\u0456 \u0434\u0430\u043d\u0438\u0445, \u044f\u043a\u0438\u0439 \u0432\u043e\u043d\u0430 \u043d\u0456\u043a\u043e\u043b\u0438 \u043d\u0435 \u0431\u0430\u0447\u0438\u043b\u0430, \u043e\u0441\u043a\u0456\u043b\u044c\u043a\u0438 \u0432\u0456\u043d <a href=\"https:\/\/statorials.org\/uk\/\u043f\u0435\u0440\u0435\u043e\u0431\u043b\u0430\u0434\u043d\u0430\u043d\u043d\u044f-\u043c\u0430\u0448\u0438\u043d\u043d\u043e\u0433\u043e-\u043d\u0430\u0432\u0447\u0430\u043d\u043d\u044f\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u043f\u0435\u0440\u0435\u043f\u043e\u0432\u043d\u044e\u0454<\/a> \u043d\u0430\u0432\u0447\u0430\u043b\u044c\u043d\u0438\u0439 \u043d\u0430\u0431\u0456\u0440 \u0434\u0430\u043d\u0438\u0445. \u043d\u0430\u0432\u0447\u0430\u043b\u044c\u043d\u0438\u0439 \u043d\u0430\u0431\u0456\u0440.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u041e\u0434\u0438\u043d \u0456\u0437 \u0441\u043f\u043e\u0441\u043e\u0431\u0456\u0432 \u0432\u0438\u0440\u0456\u0448\u0438\u0442\u0438 \u0446\u044e \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0443 \u2014 \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u0430\u0442\u0438 \u043c\u0435\u0442\u043e\u0434 <a href=\"https:\/\/statorials.org\/uk\/\u0447\u0430\u0441\u0442\u043a\u043e\u0432\u0456-\u043d\u0430\u0438\u043c\u0435\u043d\u0448\u0456-\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u0447\u0430\u0441\u0442\u043a\u043e\u0432\u0438\u0445 \u043d\u0430\u0439\u043c\u0435\u043d\u0448\u0438\u0445 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0456\u0432<\/a> , \u044f\u043a\u0438\u0439 \u043f\u0440\u0430\u0446\u044e\u0454 \u043d\u0430\u0441\u0442\u0443\u043f\u043d\u0438\u043c \u0447\u0438\u043d\u043e\u043c:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u0421\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u0438\u0437\u0443\u0439\u0442\u0435 \u0437\u043c\u0456\u043d\u043d\u0456 \u043f\u0440\u043e\u0433\u043d\u043e\u0437\u0443 \u0442\u0430 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0456.<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u041e\u0431\u0447\u0438\u0441\u043b\u0456\u0442\u044c <em>M<\/em> \u043b\u0456\u043d\u0456\u0439\u043d\u0438\u0445 \u043a\u043e\u043c\u0431\u0456\u043d\u0430\u0446\u0456\u0439 (\u0437\u0432\u0430\u043d\u0438\u0445 \u00ab\u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0430\u043c\u0438 PLS\u00bb) p<\/span> <em style=\"color: #000000;\">\u043f\u043e\u0447\u0430\u0442\u043a\u043e\u0432\u0438\u0445<\/em> <span style=\"color: #000000;\">\u0437\u043c\u0456\u043d\u043d\u0438\u0445 \u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u0456\u0432, \u044f\u043a\u0456 \u043f\u043e\u044f\u0441\u043d\u044e\u044e\u0442\u044c \u0437\u043d\u0430\u0447\u043d\u0443 \u043a\u0456\u043b\u044c\u043a\u0456\u0441\u0442\u044c \u0432\u0430\u0440\u0456\u0430\u0446\u0456\u0439 \u044f\u043a \u0443 \u0437\u043c\u0456\u043d\u043d\u0456\u0439 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0456, \u0442\u0430\u043a \u0456 \u0432 \u0437\u043c\u0456\u043d\u043d\u0438\u0445 \u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u0456\u0432.<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0412\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0439\u0442\u0435 \u043c\u0435\u0442\u043e\u0434 \u043d\u0430\u0439\u043c\u0435\u043d\u0448\u0438\u0445 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0456\u0432, \u0449\u043e\u0431 \u043f\u0456\u0434\u0456\u0431\u0440\u0430\u0442\u0438 \u043c\u043e\u0434\u0435\u043b\u044c \u043b\u0456\u043d\u0456\u0439\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 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0438 PLS \u044f\u043a \u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u0438.<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0412\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0439\u0442\u0435 <a href=\"https:\/\/statorials.org\/uk\/k-\u043a\u0440\u0430\u0442\u043d\u0430-\u043f\u0435\u0440\u0435\u0445\u0440\u0435\u0441\u043d\u0430-\u043f\u0435\u0440\u0435\u0432\u0456\u0440\u043a\u0430\/\" target=\"_blank\" rel=\"noopener noreferrer\">k-\u043a\u0440\u0430\u0442\u043d\u0443 \u043f\u0435\u0440\u0435\u0445\u0440\u0435\u0441\u043d\u0443 \u043f\u0435\u0440\u0435\u0432\u0456\u0440\u043a\u0443<\/a> , \u0449\u043e\u0431 \u0437\u043d\u0430\u0439\u0442\u0438 \u043e\u043f\u0442\u0438\u043c\u0430\u043b\u044c\u043d\u0443 \u043a\u0456\u043b\u044c\u043a\u0456\u0441\u0442\u044c \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0456\u0432 PLS \u0434\u043b\u044f \u0437\u0431\u0435\u0440\u0435\u0436\u0435\u043d\u043d\u044f \u0432 \u043c\u043e\u0434\u0435\u043b\u0456.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u0426\u0435\u0439 \u043f\u0456\u0434\u0440\u0443\u0447\u043d\u0438\u043a \u043d\u0430\u0434\u0430\u0454 \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\u043d\u0443\u0432\u0430\u0442\u0438 \u0447\u0430\u0441\u0442\u043a\u043e\u0432\u0456 \u043d\u0430\u0439\u043c\u0435\u043d\u0448\u0456 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438 \u0432 Python.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u041a\u0440\u043e\u043a 1. \u0406\u043c\u043f\u043e\u0440\u0442\u0443\u0439\u0442\u0435 \u043d\u0435\u043e\u0431\u0445\u0456\u0434\u043d\u0456 \u043f\u0430\u043a\u0435\u0442\u0438<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0421\u043f\u043e\u0447\u0430\u0442\u043a\u0443 \u043c\u0438 \u0456\u043c\u043f\u043e\u0440\u0442\u0443\u0454\u043c\u043e \u043f\u0430\u043a\u0435\u0442\u0438, \u043d\u0435\u043e\u0431\u0445\u0456\u0434\u043d\u0456 \u0434\u043b\u044f \u0432\u0438\u043a\u043e\u043d\u0430\u043d\u043d\u044f \u0447\u0430\u0441\u0442\u043a\u043e\u0432\u0438\u0445 \u043d\u0430\u0439\u043c\u0435\u043d\u0448\u0438\u0445 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0456\u0432 \u0443 Python:<\/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. <span style=\"color: #3366ff;\">model_selection<\/span> <span style=\"color: #008000;\">import<\/span> train_test_split\n<span style=\"color: #008000;\">from <span style=\"color: #000000;\">sklearn. <span style=\"color: #3366ff;\">cross_decomposition<\/span> <span style=\"color: #008000;\">import<\/span> PLSRegression<\/span>\n<span style=\"color: #008000;\">from<\/span> <span style=\"color: #000000;\">sklearn<\/span> . <span style=\"color: #3366ff;\">metrics<\/span> <span style=\"color: #008000;\">import<\/span> <span style=\"color: #000000;\">mean_squared_error\n<\/span><\/span><\/strong><\/span><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>\u041a\u0440\u043e\u043a 2. \u0417\u0430\u0432\u0430\u043d\u0442\u0430\u0436\u0442\u0435 \u0434\u0430\u043d\u0456<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0414\u043b\u044f \u0446\u044c\u043e\u0433\u043e \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u0443 \u043c\u0438 \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u0430\u0454\u043c\u043e \u043d\u0430\u0431\u0456\u0440 \u0434\u0430\u043d\u0438\u0445 \u043f\u0456\u0434 \u043d\u0430\u0437\u0432\u043e\u044e <strong>mtcars<\/strong> , \u044f\u043a\u0438\u0439 \u043c\u0456\u0441\u0442\u0438\u0442\u044c \u0456\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0456\u044e \u043f\u0440\u043e 33 \u0440\u0456\u0437\u043d\u0456 \u0430\u0432\u0442\u043e\u043c\u043e\u0431\u0456\u043b\u0456. \u041c\u0438 \u0431\u0443\u0434\u0435\u043c\u043e \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 <strong>hp<\/strong> \u044f\u043a \u0437\u043c\u0456\u043d\u043d\u0443 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0456 \u0442\u0430 \u043d\u0430\u0441\u0442\u0443\u043f\u043d\u0456 \u0437\u043c\u0456\u043d\u043d\u0456 \u044f\u043a \u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u0438:<\/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;\">\u0434\u0438\u0441\u043f\u043b\u0435\u0439<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u043b\u0430\u0439\u043d\u043e<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0432\u0430\u0433\u0430<\/span><\/li>\n<li> <span style=\"color: #000000;\">qsec<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u041d\u0430\u0441\u0442\u0443\u043f\u043d\u0438\u0439 \u043a\u043e\u0434 \u043f\u043e\u043a\u0430\u0437\u0443\u0454, \u044f\u043a \u0437\u0430\u0432\u0430\u043d\u0442\u0430\u0436\u0438\u0442\u0438 \u0442\u0430 \u0432\u0456\u0434\u043e\u0431\u0440\u0430\u0437\u0438\u0442\u0438 \u0446\u0435\u0439 \u043d\u0430\u0431\u0456\u0440 \u0434\u0430\u043d\u0438\u0445:<\/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>\u041a\u0440\u043e\u043a 3. \u041f\u0456\u0434\u0431\u0435\u0440\u0456\u0442\u044c \u0447\u0430\u0441\u0442\u043a\u043e\u0432\u0443 \u043c\u043e\u0434\u0435\u043b\u044c \u043d\u0430\u0439\u043c\u0435\u043d\u0448\u0438\u0445 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0456\u0432<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">\u041d\u0430\u0441\u0442\u0443\u043f\u043d\u0438\u0439 \u043a\u043e\u0434 \u043f\u043e\u043a\u0430\u0437\u0443\u0454, \u044f\u043a \u043f\u0456\u0434\u0456\u0433\u043d\u0430\u0442\u0438 \u043c\u043e\u0434\u0435\u043b\u044c PLS \u0434\u043e \u0446\u0438\u0445 \u0434\u0430\u043d\u0438\u0445.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0417\u0432\u0435\u0440\u043d\u0456\u0442\u044c \u0443\u0432\u0430\u0433\u0443, \u0449\u043e<\/span> <span style=\"color: #000000;\"><strong>cv = RepeatedKFold()<\/strong> \u0432\u043a\u0430\u0437\u0443\u0454 Python \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 <a href=\"https:\/\/statorials.org\/uk\/k-\u043a\u0440\u0430\u0442\u043d\u0430-\u043f\u0435\u0440\u0435\u0445\u0440\u0435\u0441\u043d\u0430-\u043f\u0435\u0440\u0435\u0432\u0456\u0440\u043a\u0430\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u043f\u0435\u0440\u0435\u0445\u0440\u0435\u0441\u043d\u0443 \u043f\u0435\u0440\u0435\u0432\u0456\u0440\u043a\u0443 k-\u0437\u0433\u043e\u0440\u0442\u043a\u0438<\/a> \u0434\u043b\u044f \u043e\u0446\u0456\u043d\u043a\u0438 \u043f\u0440\u043e\u0434\u0443\u043a\u0442\u0438\u0432\u043d\u043e\u0441\u0442\u0456 \u043c\u043e\u0434\u0435\u043b\u0456. \u0414\u043b\u044f \u0446\u044c\u043e\u0433\u043e \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u0443 \u043c\u0438 \u0432\u0438\u0431\u0438\u0440\u0430\u0454\u043c\u043e k = 10 \u0437\u0433\u043e\u0440\u0442\u043e\u043a, \u043f\u043e\u0432\u0442\u043e\u0440\u0435\u043d\u0438\u0445 3 \u0440\u0430\u0437\u0438.<\/span> <\/p>\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;\">#define cross-validation method\n<span style=\"color: #000000;\">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\nmse = []\nn = <span style=\"color: #3366ff;\">len<\/span> (X)<\/span>\n\n# Calculate MSE with only the intercept\n<span style=\"color: #000000;\">score = -1*model_selection. <span style=\"color: #3366ff;\">cross_val_score<\/span> (PLSRegression(n_components=1),<\/span>\n<span style=\"color: #000000;\">n.p. <span style=\"color: #3366ff;\">ones<\/span> ((n,1)), y, cv=cv, scoring=' <span style=\"color: #008000;\">neg_mean_squared_error<\/span> '). <span style=\"color: #3366ff;\">mean<\/span> ()    \nmse. <span style=\"color: #3366ff;\">append<\/span> (score)<\/span>\n\n# Calculate MSE using cross-validation, adding one component at a time\n<span style=\"color: #000000;\"><span style=\"color: #008000;\">for<\/span> i <span style=\"color: #008000;\">in<\/span> np. <span style=\"color: #3366ff;\">arange<\/span> (1, 6):\n    pls = PLSRegression(n_components=i)\n    score = -1*model_selection. <span style=\"color: #3366ff;\">cross_val_score<\/span> (pls, scale(X), y, cv=cv,\n               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)<\/span>\n\n#plot test MSE vs. number of components\n<span style=\"color: #000000;\">plt. <span style=\"color: #3366ff;\">plot<\/span> (mse)\nplt. <span style=\"color: #3366ff;\">xlabel<\/span> (' <span style=\"color: #008000;\">Number of PLS Components<\/span> ')\nplt. <span style=\"color: #3366ff;\">ylabel<\/span> (' <span style=\"color: #008000;\">MSE<\/span> ')\nplt. <span style=\"color: #3366ff;\">title<\/span> (' <span style=\"color: #008000;\">hp<\/span> ')<\/span>\n<\/span><\/strong><\/span><\/pre>\n<h3><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11985 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/svppython1.png\" alt=\"\u0427\u0430\u0441\u0442\u043a\u043e\u0432\u0438\u0439 \u043c\u0435\u0442\u043e\u0434 \u043d\u0430\u0439\u043c\u0435\u043d\u0448\u0438\u0445 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0456\u0432 \u0443 \u0433\u0440\u0430\u0444\u0456\u043a\u0443 \u043f\u0435\u0440\u0435\u0445\u0440\u0435\u0441\u043d\u043e\u0457 \u043f\u0435\u0440\u0435\u0432\u0456\u0440\u043a\u0438 Python\" width=\"405\" height=\"284\" srcset=\"\" sizes=\"\"><\/h3>\n<p> <span style=\"color: #000000;\">\u041d\u0430 \u0433\u0440\u0430\u0444\u0456\u043a\u0443 \u0432\u0456\u0434\u043e\u0431\u0440\u0430\u0436\u0430\u0454\u0442\u044c\u0441\u044f \u043a\u0456\u043b\u044c\u043a\u0456\u0441\u0442\u044c \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0456\u0432 PLS \u043f\u043e \u043e\u0441\u0456 \u0430\u0431\u0441\u0446\u0438\u0441 \u0456 \u0442\u0435\u0441\u0442 MSE (\u0441\u0435\u0440\u0435\u0434\u043d\u044f \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u0430 \u043f\u043e\u043c\u0438\u043b\u043a\u0430) \u043f\u043e \u043e\u0441\u0456 \u0443.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u041d\u0430 \u0433\u0440\u0430\u0444\u0456\u043a\u0443 \u043c\u0438 \u0431\u0430\u0447\u0438\u043c\u043e, \u0449\u043e MSE \u0442\u0435\u0441\u0442\u0443 \u0437\u043c\u0435\u043d\u0448\u0443\u0454\u0442\u044c\u0441\u044f \u043f\u0440\u0438 \u0434\u043e\u0434\u0430\u0432\u0430\u043d\u043d\u0456 \u0434\u0432\u043e\u0445 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0456\u0432 PLS, \u0430\u043b\u0435 \u043f\u043e\u0447\u0438\u043d\u0430\u0454 \u0437\u0431\u0456\u043b\u044c\u0448\u0443\u0432\u0430\u0442\u0438\u0441\u044f, \u043a\u043e\u043b\u0438 \u043c\u0438 \u0434\u043e\u0434\u0430\u0454\u043c\u043e \u0431\u0456\u043b\u044c\u0448\u0435 \u0434\u0432\u043e\u0445 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0456\u0432 PLS.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0422\u0430\u043a\u0438\u043c \u0447\u0438\u043d\u043e\u043c, \u043e\u043f\u0442\u0438\u043c\u0430\u043b\u044c\u043d\u0430 \u043c\u043e\u0434\u0435\u043b\u044c \u0432\u043a\u043b\u044e\u0447\u0430\u0454 \u043b\u0438\u0448\u0435 \u043f\u0435\u0440\u0448\u0456 \u0434\u0432\u0430 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0438 PLS.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u041a\u0440\u043e\u043a 4. \u0412\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0439\u0442\u0435 \u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u0443 \u043c\u043e\u0434\u0435\u043b\u044c \u0434\u043b\u044f \u043f\u0440\u043e\u0433\u043d\u043e\u0437\u0443\u0432\u0430\u043d\u043d\u044f<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u041c\u0438 \u043c\u043e\u0436\u0435\u043c\u043e \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u0443 \u043c\u043e\u0434\u0435\u043b\u044c PLS \u0456\u0437 \u0434\u0432\u043e\u043c\u0430 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0430\u043c\u0438 PLS, \u0449\u043e\u0431 \u0440\u043e\u0431\u0438\u0442\u0438 \u043f\u0440\u043e\u0433\u043d\u043e\u0437\u0438 \u0449\u043e\u0434\u043e \u043d\u043e\u0432\u0438\u0445 \u0441\u043f\u043e\u0441\u0442\u0435\u0440\u0435\u0436\u0435\u043d\u044c.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\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 \u0440\u043e\u0437\u0434\u0456\u043b\u0438\u0442\u0438 \u0432\u0438\u0445\u0456\u0434\u043d\u0438\u0439 \u043d\u0430\u0431\u0456\u0440 \u0434\u0430\u043d\u0438\u0445 \u043d\u0430 \u043d\u0430\u0432\u0447\u0430\u043b\u044c\u043d\u0438\u0439 \u0456 \u0442\u0435\u0441\u0442\u043e\u0432\u0438\u0439 \u043d\u0430\u0431\u0456\u0440 \u0456 \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u043c\u043e\u0434\u0435\u043b\u044c PLS \u0456\u0437 \u0434\u0432\u043e\u043c\u0430 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0430\u043c\u0438 PLS \u0434\u043b\u044f \u043f\u0440\u043e\u0433\u043d\u043e\u0437\u0443\u0432\u0430\u043d\u043d\u044f \u043d\u0430 \u0442\u0435\u0441\u0442\u043e\u0432\u043e\u043c\u0443 \u043d\u0430\u0431\u043e\u0440\u0456.<\/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><span style=\"color: #3366ff;\">X_train<\/span> <span style=\"color: #008000;\">,<\/span> <span style=\"color: #008000;\">_<\/span><span style=\"color: #008080;\">\n\n#calculate RMSE\n<span style=\"color: #000000;\">pls = PLSRegression(n_components=2)\npls. <span style=\"color: #3366ff;\">fit<\/span> (scale(X_train), y_train)<\/span>\n\n<span style=\"color: #000000;\">n.p. <span style=\"color: #3366ff;\">sqrt<\/span> (mean_squared_error(y_test, pls. <span style=\"color: #3366ff;\">predict<\/span> (scale(X_test))))\n<\/span>\n<span style=\"color: #000000;\">29.9094\n<\/span><\/span><\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">\u041c\u0438 \u0431\u0430\u0447\u0438\u043c\u043e, \u0449\u043e RMSE \u0442\u0435\u0441\u0442\u0443 \u0432\u0438\u044f\u0432\u043b\u044f\u0454\u0442\u044c\u0441\u044f <strong>29,9094<\/strong> . \u0426\u0435 \u0441\u0435\u0440\u0435\u0434\u043d\u0454 \u0432\u0456\u0434\u0445\u0438\u043b\u0435\u043d\u043d\u044f \u043c\u0456\u0436 \u043f\u0440\u043e\u0433\u043d\u043e\u0437\u043e\u0432\u0430\u043d\u0438\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f\u043c <em>hp<\/em> \u0456 \u0441\u043f\u043e\u0441\u0442\u0435\u0440\u0435\u0436\u0443\u0432\u0430\u043d\u0438\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f\u043c <em>hp<\/em> \u0434\u043b\u044f \u0441\u043f\u043e\u0441\u0442\u0435\u0440\u0435\u0436\u0435\u043d\u044c \u0442\u0435\u0441\u0442\u043e\u0432\u043e\u0433\u043e \u043d\u0430\u0431\u043e\u0440\u0443.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u041f\u043e\u0432\u043d\u0438\u0439 \u043a\u043e\u0434 Python, \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u0430\u043d\u0438\u0439 \u0443 \u0446\u044c\u043e\u043c\u0443 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u0456, \u043c\u043e\u0436\u043d\u0430 \u0437\u043d\u0430\u0439\u0442\u0438 <a href=\"https:\/\/github.com\/Statorials\/Python-Guides\/blob\/main\/partial_least_squares.py\" target=\"_blank\" rel=\"noopener noreferrer\">\u0442\u0443\u0442<\/a> .<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u041e\u0434\u043d\u0430 \u0437 \u043d\u0430\u0439\u043f\u043e\u0448\u0438\u0440\u0435\u043d\u0456\u0448\u0438\u0445 \u043f\u0440\u043e\u0431\u043b\u0435\u043c, \u0437 \u044f\u043a\u043e\u044e \u0432\u0438 \u0437\u0456\u0442\u043a\u043d\u0435\u0442\u0435\u0441\u044f \u043f\u0456\u0434 \u0447\u0430\u0441 \u043c\u0430\u0448\u0438\u043d\u043d\u043e\u0433\u043e \u043d\u0430\u0432\u0447\u0430\u043d\u043d\u044f, \u2014 \u043c\u0443\u043b\u044c\u0442\u0438\u043a\u043e\u043b\u0456\u043d\u0435\u0430\u0440\u043d\u0456\u0441\u0442\u044c . \u0426\u0435 \u0432\u0456\u0434\u0431\u0443\u0432\u0430\u0454\u0442\u044c\u0441\u044f, \u043a\u043e\u043b\u0438 \u0434\u0432\u0456 \u0430\u0431\u043e \u0431\u0456\u043b\u044c\u0448\u0435 \u0437\u043c\u0456\u043d\u043d\u0438\u0445 \u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u0430 \u0432 \u043d\u0430\u0431\u043e\u0440\u0456 \u0434\u0430\u043d\u0438\u0445 \u0441\u0438\u043b\u044c\u043d\u043e \u043a\u043e\u0440\u0435\u043b\u044c\u043e\u0432\u0430\u043d\u0456. \u041a\u043e\u043b\u0438 \u0446\u0435 \u0442\u0440\u0430\u043f\u043b\u044f\u0454\u0442\u044c\u0441\u044f, \u043c\u043e\u0434\u0435\u043b\u044c \u043c\u043e\u0436\u0435 \u0434\u043e\u0431\u0440\u0435 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0430\u0442\u0438 \u043d\u0430\u0432\u0447\u0430\u043b\u044c\u043d\u043e\u043c\u0443 \u043d\u0430\u0431\u043e\u0440\u0443 \u0434\u0430\u043d\u0438\u0445, \u0430\u043b\u0435 \u043c\u043e\u0436\u0435 \u043f\u0440\u0430\u0446\u044e\u0432\u0430\u0442\u0438 \u043f\u043e\u0433\u0430\u043d\u043e \u043d\u0430 \u043d\u043e\u0432\u043e\u043c\u0443 \u043d\u0430\u0431\u043e\u0440\u0456 \u0434\u0430\u043d\u0438\u0445, \u044f\u043a\u0438\u0439 \u0432\u043e\u043d\u0430 \u043d\u0456\u043a\u043e\u043b\u0438 \u043d\u0435 \u0431\u0430\u0447\u0438\u043b\u0430, \u043e\u0441\u043a\u0456\u043b\u044c\u043a\u0438 \u0432\u0456\u043d \u043f\u0435\u0440\u0435\u043f\u043e\u0432\u043d\u044e\u0454 \u043d\u0430\u0432\u0447\u0430\u043b\u044c\u043d\u0438\u0439 [&hellip;]<\/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":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0427\u0430\u0441\u0442\u043a\u043e\u0432\u0456 \u043d\u0430\u0439\u043c\u0435\u043d\u0448\u0456 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438 \u0432 Python (\u043a\u0440\u043e\u043a \u0437\u0430 \u043a\u0440\u043e\u043a\u043e\u043c) - \u0421\u0442\u0430\u0442\u043e\u043b\u043e\u0433\u0456\u044f<\/title>\n<meta name=\"description\" content=\"\u0426\u0435\u0439 \u043f\u0456\u0434\u0440\u0443\u0447\u043d\u0438\u043a \u043f\u043e\u044f\u0441\u043d\u044e\u0454, \u044f\u043a 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