{"id":1191,"date":"2023-07-27T08:19:55","date_gmt":"2023-07-27T08:19:55","guid":{"rendered":"https:\/\/statorials.org\/ru\/%d0%b3%d1%80%d0%b5%d0%b1%d0%b5%d0%bd%d1%8c-%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81%d1%81%d0%b8%d0%b8-%d0%b2-r\/"},"modified":"2023-07-27T08:19:55","modified_gmt":"2023-07-27T08:19:55","slug":"%d0%b3%d1%80%d0%b5%d0%b1%d0%b5%d0%bd%d1%8c-%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81%d1%81%d0%b8%d0%b8-%d0%b2-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/ru\/%d0%b3%d1%80%d0%b5%d0%b1%d0%b5%d0%bd%d1%8c-%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81%d1%81%d0%b8%d0%b8-%d0%b2-r\/","title":{"rendered":"\u0420\u0438\u0434\u0436-\u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f \u0432 r (\u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/ru\/\u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f-\u0433\u0440\u0435\u0431\u043d\u044f\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u0420\u0438\u0434\u0436-\u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f<\/a> \u2014 \u044d\u0442\u043e \u043c\u0435\u0442\u043e\u0434, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0434\u043b\u044f \u043f\u043e\u0434\u0431\u043e\u0440\u0430 \u043c\u043e\u0434\u0435\u043b\u0438 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438, \u043a\u043e\u0433\u0434\u0430 \u0432 \u0434\u0430\u043d\u043d\u044b\u0445 \u043f\u0440\u0438\u0441\u0443\u0442\u0441\u0442\u0432\u0443\u0435\u0442 <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><\/p>\n<p> <span style=\"color: #000000;\">\u041a\u043e\u0440\u043e\u0447\u0435 \u0433\u043e\u0432\u043e\u0440\u044f, \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f \u043d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0438\u0445 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432 \u043f\u044b\u0442\u0430\u0435\u0442\u0441\u044f \u043d\u0430\u0439\u0442\u0438 \u043e\u0446\u0435\u043d\u043a\u0438 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u0432, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u0438\u043d\u0438\u043c\u0438\u0437\u0438\u0440\u0443\u044e\u0442 \u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u0443\u044e \u0441\u0443\u043c\u043c\u0443 \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> )2<\/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;\">\u0418 \u043d\u0430\u043e\u0431\u043e\u0440\u043e\u0442, \u0433\u0440\u0435\u0431\u043d\u0435\u0432\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0441\u044f \u0441\u0432\u0435\u0441\u0442\u0438 \u043a \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u0443 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>RSS + \u03bb\u03a3\u03b2 <sub>j<\/sub> <sup>2<\/sup><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0433\u0434\u0435 <em>j<\/em> \u0438\u0437\u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \u043e\u0442 1 \u0434\u043e <em>p<\/em> \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445-\u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u043e\u0432 \u0438 \u03bb \u2265 0.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u042d\u0442\u043e\u0442 \u0432\u0442\u043e\u0440\u043e\u0439 \u0447\u043b\u0435\u043d \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438 \u0438\u0437\u0432\u0435\u0441\u0442\u0435\u043d \u043a\u0430\u043a <em>\u0448\u0442\u0440\u0430\u0444 \u0437\u0430 \u0441\u043d\u044f\u0442\u0438\u0435 \u0441\u0440\u0435\u0434\u0441\u0442\u0432<\/em> . \u0412 \u0433\u0440\u0435\u0431\u043d\u0435\u0432\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u043c\u044b \u0432\u044b\u0431\u0438\u0440\u0430\u0435\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u03bb, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0434\u0430\u0435\u0442 \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u043e \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0439 \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).<\/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 \u0433\u0440\u0435\u0431\u043d\u0435\u0432\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u0432 R.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u0428\u0430\u0433 1. \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 \u0432\u0441\u0442\u0440\u043e\u0435\u043d\u043d\u044b\u0439 \u043d\u0430\u0431\u043e\u0440 \u0434\u0430\u043d\u043d\u044b\u0445 R \u043f\u043e\u0434 \u043d\u0430\u0437\u0432\u0430\u043d\u0438\u0435\u043c <strong>mtcars<\/strong> . \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;\">\u043c\u0430\u0441\u0441\u0430<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0434\u0435\u0440\u044c\u043c\u043e<\/span><\/li>\n<li> <span style=\"color: #000000;\">qsec<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u0414\u043b\u044f \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u0438\u044f \u0440\u0438\u0434\u0436-\u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438\u0437 \u043f\u0430\u043a\u0435\u0442\u0430 <strong>glmnet<\/strong> . \u042d\u0442\u043e\u0442 \u043f\u0430\u043a\u0435\u0442 \u0442\u0440\u0435\u0431\u0443\u0435\u0442, \u0447\u0442\u043e\u0431\u044b <a href=\"https:\/\/statorials.org\/ru\/\u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0435-\u043f\u043e\u044f\u0441\u043d\u044f\u044e\u0449\u0438\u0435-\u043e\u0442\u0432\u0435\u0442\u044b\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0430\u044f \u043e\u0442\u0432\u0435\u0442\u0430<\/a> \u0431\u044b\u043b\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u043c, \u0430 \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 \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0430\u043b \u043a \u043a\u043b\u0430\u0441\u0441\u0443 <strong>data.matrix<\/strong> .<\/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 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u043d\u0430\u0448\u0438 \u0434\u0430\u043d\u043d\u044b\u0435:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#define response variable<\/span>\ny &lt;- mtcars$hp\n\n<span style=\"color: #008080;\">#define matrix of predictor variables\n<\/span>x &lt;- data.matrix(mtcars[, c('mpg', 'wt', 'drat', 'qsec')])\n<\/strong><\/span><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>\u0428\u0430\u0433 2. \u041f\u043e\u0434\u0431\u043e\u0440 \u043c\u043e\u0434\u0435\u043b\u0438 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u0440\u0438\u0434\u0436\u0430<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0414\u0430\u043b\u0435\u0435 \u043c\u044b \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0441\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439 <strong>glmnet()<\/strong> , \u0447\u0442\u043e\u0431\u044b \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u043e\u0432\u0430\u0442\u044c \u043c\u043e\u0434\u0435\u043b\u0438 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u0420\u0438\u0434\u0436\u0430, \u0438 \u0443\u043a\u0430\u0436\u0435\u043c <strong>\u0430\u043b\u044c\u0444\u0430=0<\/strong> .<\/span><\/p>\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 \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0430 \u0430\u043b\u044c\u0444\u0430, \u0440\u0430\u0432\u043d\u0430\u044f 1, \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u0430 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044e \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u041b\u0430\u0441\u0441\u043e, \u0430 \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0430 \u0430\u043b\u044c\u0444\u0430 \u043d\u0430 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043e\u0442 0 \u0434\u043e 1 \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u0430 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044e \u044d\u043b\u0430\u0441\u0442\u0438\u0447\u043d\u043e\u0439 \u0441\u0435\u0442\u0438.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0422\u0430\u043a\u0436\u0435 \u043e\u0431\u0440\u0430\u0442\u0438\u0442\u0435 \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435, \u0447\u0442\u043e \u0433\u0440\u0435\u0431\u043d\u0435\u0432\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f \u0442\u0440\u0435\u0431\u0443\u0435\u0442, \u0447\u0442\u043e\u0431\u044b \u0434\u0430\u043d\u043d\u044b\u0435 \u0431\u044b\u043b\u0438 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u043d\u044b \u0442\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0447\u0442\u043e\u0431\u044b \u043a\u0430\u0436\u0434\u0430\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0430\u044f-\u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440 \u0438\u043c\u0435\u043b\u0430 \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.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u041a \u0441\u0447\u0430\u0441\u0442\u044c\u044e, <strong>glmnet()<\/strong> \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442 \u044d\u0442\u0443 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u0438\u0437\u0430\u0446\u0438\u044e \u0437\u0430 \u0432\u0430\u0441. \u0415\u0441\u043b\u0438 \u0432\u044b \u0443\u0436\u0435 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u043b\u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0435, \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u043a\u0430\u0437\u0430\u0442\u044c <strong>\u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c=False<\/strong> .<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #993300;\">library<\/span> (glmnet)<\/span>\n\n#fit ridge regression model\n<\/span>model &lt;- glmnet(x, y, alpha = <span style=\"color: #008000;\">0<\/span> )\n\n<span style=\"color: #008080;\">#view summary of model\n<\/span>summary(model)\n\n          Length Class Mode   \na0 100 -none- numeric\nbeta 400 dgCMatrix S4     \ndf 100 -none- numeric\ndim 2 -none- numeric\nlambda 100 -none- numeric\ndev.ratio 100 -none- numeric\nnulldev 1 -none- numeric\nnpasses 1 -none- numeric\njerr 1 -none- numeric\noffset 1 -none- logical\ncall 4 -none- call   \nnobs 1 -none- numeric\n<\/strong><\/span><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>\u0428\u0430\u0433&nbsp;3. \u0412\u044b\u0431\u0435\u0440\u0438\u0442\u0435 \u043e\u043f\u0442\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043b\u044f\u043c\u0431\u0434\u044b.<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0414\u0430\u043b\u0435\u0435 \u043c\u044b \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043b\u044f\u043c\u0431\u0434\u0430, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0434\u0430\u0435\u0442 \u043d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0443\u044e \u0441\u0440\u0435\u0434\u043d\u0435\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u043e\u0448\u0438\u0431\u043a\u0443 \u0442\u0435\u0441\u0442\u0430 (MSE), \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f <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\">k-\u043a\u0440\u0430\u0442\u043d\u0443\u044e \u043f\u0435\u0440\u0435\u043a\u0440\u0435\u0441\u0442\u043d\u0443\u044e \u043f\u0440\u043e\u0432\u0435\u0440\u043a\u0443<\/a> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u041a \u0441\u0447\u0430\u0441\u0442\u044c\u044e, <strong>\u0432 glmnet<\/strong> \u0435\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u044f <strong>cv.glmnet()<\/strong> , \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442 k-\u043a\u0440\u0430\u0442\u043d\u0443\u044e \u043f\u0435\u0440\u0435\u043a\u0440\u0435\u0441\u0442\u043d\u0443\u044e \u043f\u0440\u043e\u0432\u0435\u0440\u043a\u0443, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f k = 10 \u0440\u0430\u0437.<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#perform k-fold cross-validation to find optimal lambda value\n<\/span>cv_model &lt;- cv. <span style=\"color: #3366ff;\">glmnet<\/span> (x, y, alpha = <span style=\"color: #008000;\">0<\/span> )\n\n<span style=\"color: #008080;\">#find optimal lambda value that minimizes test MSE\n<\/span>best_lambda &lt;- cv_model$ <span style=\"color: #3366ff;\">lambda<\/span> . <span style=\"color: #3366ff;\">min<\/span>\nbest_lambda\n\n[1] 10.04567\n\n<span style=\"color: #008080;\">#produce plot of test MSE by lambda value<\/span>\nplot(cv_model) \n<\/strong><\/span><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11860 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/faiter1.png\" alt=\"\u043f\u0435\u0440\u0435\u043a\u0440\u0435\u0441\u0442\u043d\u0430\u044f \u043f\u0440\u043e\u0432\u0435\u0440\u043a\u0430 \u0434\u043b\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u0433\u0440\u0435\u0431\u043d\u044f \u0432 R\" width=\"443\" height=\"426\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u0417\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043b\u044f\u043c\u0431\u0434\u0430, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043c\u0438\u043d\u0438\u043c\u0438\u0437\u0438\u0440\u0443\u0435\u0442 \u0442\u0435\u0441\u0442 MSE, \u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0440\u0430\u0432\u043d\u044b\u043c <strong>10,04567<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u0428\u0430\u0433 4. \u0410\u043d\u0430\u043b\u0438\u0437 \u043e\u043a\u043e\u043d\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u043c\u043e\u0434\u0435\u043b\u0438<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043f\u0440\u043e\u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u043e\u043a\u043e\u043d\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u0443\u044e \u043c\u043e\u0434\u0435\u043b\u044c, \u0441\u043e\u0437\u0434\u0430\u043d\u043d\u0443\u044e \u043f\u043e \u043e\u043f\u0442\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u043c\u0443 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044e \u043b\u044f\u043c\u0431\u0434\u0430.<\/span><\/p>\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 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u043a\u043e\u0434 \u0434\u043b\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u043e\u0446\u0435\u043d\u043e\u043a \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u0432 \u0434\u043b\u044f \u044d\u0442\u043e\u0439 \u043c\u043e\u0434\u0435\u043b\u0438:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#find coefficients of best model\n<\/span>best_model &lt;- glmnet(x, y, alpha = <span style=\"color: #008000;\">0<\/span> , lambda = best_lambda)\ncoef(best_model)\n\n5 x 1 sparse Matrix of class \"dgCMatrix\"\n                    s0\n(Intercept) 475.242646\nmpg -3.299732\nwt 19.431238\ndrat -1.222429\nqsec -17.949721<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">\u041c\u044b \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u0435\u043c \u0441\u043e\u0437\u0434\u0430\u0442\u044c \u0433\u0440\u0430\u0444\u0438\u043a \u0442\u0440\u0430\u0441\u0441\u0438\u0440\u043e\u0432\u043a\u0438, \u0447\u0442\u043e\u0431\u044b \u0432\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c, \u043a\u0430\u043a \u0438\u0437\u043c\u0435\u043d\u0438\u043b\u0438\u0441\u044c \u043e\u0446\u0435\u043d\u043a\u0438 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u0432 \u0438\u0437-\u0437\u0430 \u0443\u0432\u0435\u043b\u0438\u0447\u0435\u043d\u0438\u044f \u043b\u044f\u043c\u0431\u0434\u0430:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#produce Ridge trace plot<\/span>\nplot(model, xvar = \" <span style=\"color: #008000;\">lambda<\/span> \")<\/strong><\/span> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11861 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/creter2.png\" alt=\"\u0421\u043b\u0435\u0434 \u0445\u0440\u0435\u0431\u0442\u0430 \u0432 R\" width=\"419\" height=\"411\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0442\u044c <a href=\"https:\/\/statorials.org\/ru\/\u0445\u043e\u0440\u043e\u0448\u0435\u0435-\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435-r-\u0432-\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435\/\" target=\"_blank\" rel=\"noopener noreferrer\">R-\u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u043c\u043e\u0434\u0435\u043b\u0438<\/a> \u043d\u0430 \u043e\u0431\u0443\u0447\u0430\u044e\u0449\u0438\u0445 \u0434\u0430\u043d\u043d\u044b\u0445:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#use fitted best model to make predictions\n<\/span>y_predicted &lt;- <span style=\"color: #3366ff;\">predict<\/span> (model, s = best_lambda, newx = x)\n\n<span style=\"color: #008080;\">#find OHS and SSE<\/span>\nsst &lt;- <span style=\"color: #3366ff;\">sum<\/span> ((y - <span style=\"color: #3366ff;\">mean<\/span> (y))^2)\nsse &lt;- <span style=\"color: #3366ff;\">sum<\/span> ((y_predicted - y)^2)\n\n<span style=\"color: #008080;\">#find R-Squared\n<\/span>rsq &lt;- 1 - sse\/sst\nrsq\n\n[1] 0.7999513\n<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">\u041a\u0432\u0430\u0434\u0440\u0430\u0442 R \u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0440\u0430\u0432\u043d\u044b\u043c <strong>0,7999513<\/strong> . \u0422\u043e \u0435\u0441\u0442\u044c \u043b\u0443\u0447\u0448\u0430\u044f \u043c\u043e\u0434\u0435\u043b\u044c \u0441\u043c\u043e\u0433\u043b\u0430 \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u0442\u044c <strong>79,99%<\/strong> \u0432\u0430\u0440\u0438\u0430\u0446\u0438\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u043e\u0442\u0432\u0435\u0442\u0430 \u043e\u0431\u0443\u0447\u0430\u044e\u0449\u0438\u0445 \u0434\u0430\u043d\u043d\u044b\u0445.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u041f\u043e\u043b\u043d\u044b\u0439 \u043a\u043e\u0434 R, \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, \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u043d\u0430\u0439\u0442\u0438 <a href=\"https:\/\/github.com\/Statorials\/R-Guides\/blob\/main\/ridge_regression.R\" target=\"_blank\" rel=\"noopener noreferrer\">\u0437\u0434\u0435\u0441\u044c<\/a> .<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0420\u0438\u0434\u0436-\u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f \u2014 \u044d\u0442\u043e \u043c\u0435\u0442\u043e\u0434, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0434\u043b\u044f \u043f\u043e\u0434\u0431\u043e\u0440\u0430 \u043c\u043e\u0434\u0435\u043b\u0438 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438, \u043a\u043e\u0433\u0434\u0430 \u0432 \u0434\u0430\u043d\u043d\u044b\u0445 \u043f\u0440\u0438\u0441\u0443\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u043c\u0443\u043b\u044c\u0442\u0438\u043a\u043e\u043b\u043b\u0438\u043d\u0435\u0430\u0440\u043d\u043e\u0441\u0442\u044c . \u041a\u043e\u0440\u043e\u0447\u0435 \u0433\u043e\u0432\u043e\u0440\u044f, \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f \u043d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0438\u0445 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432 \u043f\u044b\u0442\u0430\u0435\u0442\u0441\u044f \u043d\u0430\u0439\u0442\u0438 \u043e\u0446\u0435\u043d\u043a\u0438 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u0432, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u0438\u043d\u0438\u043c\u0438\u0437\u0438\u0440\u0443\u044e\u0442 \u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u0443\u044e \u0441\u0443\u043c\u043c\u0443 \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 [&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-1191","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\/ 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