{"id":473,"date":"2023-07-29T19:05:27","date_gmt":"2023-07-29T19:05:27","guid":{"rendered":"https:\/\/statorials.org\/ru\/%d0%bf%d0%be%d0%bb%d0%b8%d0%bd%d0%be%d0%bc%d0%b8%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0%d1%8f-%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81%d1%81%d0%b8%d1%8f-r\/"},"modified":"2023-07-29T19:05:27","modified_gmt":"2023-07-29T19:05:27","slug":"%d0%bf%d0%be%d0%bb%d0%b8%d0%bd%d0%be%d0%bc%d0%b8%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0%d1%8f-%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81%d1%81%d0%b8%d1%8f-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/ru\/%d0%bf%d0%be%d0%bb%d0%b8%d0%bd%d0%be%d0%bc%d0%b8%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0%d1%8f-%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81%d1%81%d0%b8%d1%8f-r\/","title":{"rendered":"\u041f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \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\/\u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f-\u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f-1\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u041f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \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, \u043a\u043e\u0433\u0434\u0430 \u0441\u0432\u044f\u0437\u044c \u043c\u0435\u0436\u0434\u0443 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439-\u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u043e\u043c \u0438 <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\u043e\u0439 \u043e\u0442\u0432\u0435\u0442\u0430<\/a> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u042d\u0442\u043e\u0442 \u0442\u0438\u043f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u043f\u0440\u0438\u043d\u0438\u043c\u0430\u0435\u0442 \u0444\u043e\u0440\u043c\u0443:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Y = \u03b2 <sub>0<\/sub> <sup>+<\/sup> \u03b2 <sub>1<\/sub> X + \u03b2 <sub>2<\/sub> X <sup>2<\/sup> + \u2026 + \u03b2 <sub>h<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0433\u0434\u0435 <em>h<\/em> \u2014 \u00ab\u0441\u0442\u0435\u043f\u0435\u043d\u044c\u00bb \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\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 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\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&nbsp;1. \u0421\u043e\u0437\u0434\u0430\u0439\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 \u0441\u043e\u0437\u0434\u0430\u0434\u0438\u043c \u043d\u0430\u0431\u043e\u0440 \u0434\u0430\u043d\u043d\u044b\u0445, \u0441\u043e\u0434\u0435\u0440\u0436\u0430\u0449\u0438\u0439 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0438\u0437\u0443\u0447\u0435\u043d\u043d\u044b\u0445 \u0447\u0430\u0441\u043e\u0432 \u0438 \u0438\u0442\u043e\u0433\u043e\u0432\u0443\u044e \u043e\u0446\u0435\u043d\u043a\u0443 \u0437\u0430 \u044d\u043a\u0437\u0430\u043c\u0435\u043d \u0434\u043b\u044f \u043a\u043b\u0430\u0441\u0441\u0430 \u0438\u0437 50 \u0443\u0447\u0435\u043d\u0438\u043a\u043e\u0432:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#make this example reproducible<\/span>\nset.seed(1)\n\n<span style=\"color: #008080;\">#create dataset\n<\/span>df &lt;- data.frame(hours = <span style=\"color: #3366ff;\">runif<\/span> (50, 5, 15), score=50)\ndf$score = df$score + df$hours^3\/150 + df$hours* <span style=\"color: #3366ff;\">runif<\/span> (50, 1, 2)\n\n<span style=\"color: #008080;\">#view first six rows of data\n<\/span>head(data)\n\n      hours score\n1 7.655087 64.30191\n2 8.721239 70.65430\n3 10.728534 73.66114\n4 14.082078 86.14630\n5 7.016819 59.81595\n6 13.983897 83.60510\n<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>\u0428\u0430\u0433 2. \u0412\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0438\u0440\u0443\u0439\u0442\u0435 \u0434\u0430\u043d\u043d\u044b\u0435<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u041f\u0440\u0435\u0436\u0434\u0435 \u0447\u0435\u043c \u043f\u043e\u0434\u0433\u043e\u043d\u044f\u0442\u044c \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u043e\u043d\u043d\u0443\u044e \u043c\u043e\u0434\u0435\u043b\u044c \u043a \u0434\u0430\u043d\u043d\u044b\u043c, \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0441\u043e\u0437\u0434\u0430\u0434\u0438\u043c \u0434\u0438\u0430\u0433\u0440\u0430\u043c\u043c\u0443 \u0440\u0430\u0441\u0441\u0435\u044f\u043d\u0438\u044f, \u0447\u0442\u043e\u0431\u044b \u0432\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0432\u0437\u0430\u0438\u043c\u043e\u0441\u0432\u044f\u0437\u044c \u043c\u0435\u0436\u0434\u0443 \u0443\u0447\u0435\u0431\u043d\u044b\u043c\u0438 \u0447\u0430\u0441\u0430\u043c\u0438 \u0438 \u0431\u0430\u043b\u043b\u0430\u043c\u0438 \u043d\u0430 \u044d\u043a\u0437\u0430\u043c\u0435\u043d\u0435:<\/span> <\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #993300;\">library<\/span> (ggplot2)\n\nggplot(df, <span style=\"color: #3366ff;\">aes<\/span> (x=hours, y=score)) +\n  geom_point()<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12001 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/poly1-1.png\" alt=\"\" width=\"457\" height=\"450\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u041c\u044b \u0432\u0438\u0434\u0438\u043c, \u0447\u0442\u043e \u0434\u0430\u043d\u043d\u044b\u0435 \u0438\u043c\u0435\u044e\u0442 \u0441\u043b\u0435\u0433\u043a\u0430 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u0443\u044e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c, \u0447\u0442\u043e \u0443\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u043d\u0430 \u0442\u043e, \u0447\u0442\u043e \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f \u043c\u043e\u0436\u0435\u0442 \u043b\u0443\u0447\u0448\u0435 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u043e\u0432\u0430\u0442\u044c \u0434\u0430\u043d\u043d\u044b\u043c, \u0447\u0435\u043c \u043f\u0440\u043e\u0441\u0442\u0430\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">\u0428\u0430\u0433 3. \u041f\u043e\u0434\u0431\u043e\u0440 \u043c\u043e\u0434\u0435\u043b\u0435\u0439 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">\u0414\u0430\u043b\u0435\u0435 \u043c\u044b \u0430\u0434\u0430\u043f\u0442\u0438\u0440\u0443\u0435\u043c \u043f\u044f\u0442\u044c \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0445 \u043c\u043e\u0434\u0435\u043b\u0435\u0439 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u0441\u043e \u0441\u0442\u0435\u043f\u0435\u043d\u044f\u043c\u0438 <em>h<\/em> = 1\u20265 \u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c 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 \u0441 k = 10 \u0440\u0430\u0437, \u0447\u0442\u043e\u0431\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0442\u0435\u0441\u0442 MSE \u0434\u043b\u044f \u043a\u0430\u0436\u0434\u043e\u0439 \u043c\u043e\u0434\u0435\u043b\u0438:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#randomly shuffle data\n<\/span>df.shuffled &lt;- df[ <span style=\"color: #3366ff;\">sample<\/span> ( <span style=\"color: #3366ff;\">nrow<\/span> (df)),]\n\n<span style=\"color: #008080;\">#define number of folds to use for k-fold cross-validation\n<\/span>K &lt;- 10 \n\n<span style=\"color: #008080;\">#define degree of polynomials to fit\n<\/span>degree &lt;- 5\n\n<span style=\"color: #008080;\">#create k equal-sized folds\n<\/span>folds &lt;- cut( <span style=\"color: #3366ff;\">seq<\/span> (1, <span style=\"color: #3366ff;\">nrow<\/span> (df.shuffled)), breaks=K, labels= <span style=\"color: #008000;\">FALSE<\/span> )\n\n<span style=\"color: #008080;\">#create object to hold MSE's of models\n<\/span>mse = matrix(data=NA,nrow=K,ncol=degree)\n\n<span style=\"color: #008080;\">#Perform K-fold cross validation\n<\/span><span style=\"color: #008000;\">for<\/span> (i <span style=\"color: #008000;\">in<\/span> 1:K){\n    \n<span style=\"color: #008080;\">#define training and testing data\n<\/span>testIndexes &lt;- <span style=\"color: #3366ff;\">which<\/span> (folds==i,arr.ind= <span style=\"color: #008000;\">TRUE<\/span> )\n    testData &lt;- df.shuffled[testIndexes, ]\n    trainData &lt;- df.shuffled[-testIndexes, ]\n    \n<span style=\"color: #008080;\">#use k-fold cv to evaluate models\n<\/span>for (j in 1:degree){\n        fit.train = <span style=\"color: #3366ff;\">lm<\/span> (score ~ <span style=\"color: #3366ff;\">poly<\/span> (hours,d), data=trainData)\n        fit.test = <span style=\"color: #3366ff;\">predict<\/span> (fit.train, newdata=testData)\n        mse[i,j] = <span style=\"color: #3366ff;\">mean<\/span> ((fit.test-testData$score)^2) \n    }\n}\n\n<span style=\"color: #008080;\">#find MSE for each degree \n<\/span>colMeans(mse)\n\n[1] 9.802397 8.748666 9.601865 10.592569 13.545547\n<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">\u0412 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0435 \u043c\u044b \u0432\u0438\u0434\u0438\u043c \u0442\u0435\u0441\u0442 MSE \u0434\u043b\u044f \u043a\u0430\u0436\u0434\u043e\u0439 \u043c\u043e\u0434\u0435\u043b\u0438:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u0422\u0435\u0441\u0442 MSE \u0441\u043e \u0441\u0442\u0435\u043f\u0435\u043d\u044c\u044e h = 1: <strong>9,80<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0422\u0435\u0441\u0442 MSE \u0441\u043e \u0441\u0442\u0435\u043f\u0435\u043d\u044c\u044e h = 2: <strong>8,75<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0422\u0435\u0441\u0442 MSE \u0441\u043e \u0441\u0442\u0435\u043f\u0435\u043d\u044c\u044e h = 3: <strong>9,60<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0422\u0435\u0441\u0442 MSE \u0441\u043e \u0441\u0442\u0435\u043f\u0435\u043d\u044c\u044e h = 4: <strong>10,59<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0422\u0435\u0441\u0442 MSE \u0441\u043e \u0441\u0442\u0435\u043f\u0435\u043d\u044c\u044e h=5: <strong>13,55<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u041c\u043e\u0434\u0435\u043b\u044c \u0441 \u043d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0438\u043c \u0442\u0435\u0441\u0442\u043e\u0432\u044b\u043c MSE \u043e\u043a\u0430\u0437\u0430\u043b\u0430\u0441\u044c \u043c\u043e\u0434\u0435\u043b\u044c\u044e \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u0441\u043e \u0441\u0442\u0435\u043f\u0435\u043d\u044c\u044e <em>h<\/em> = 2.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u042d\u0442\u043e \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u043d\u0430\u0448\u0435\u043c\u0443 \u0438\u043d\u0442\u0443\u0438\u0442\u0438\u0432\u043d\u043e\u043c\u0443 \u0432\u044b\u0432\u043e\u0434\u0443 \u0438\u0437 \u0438\u0441\u0445\u043e\u0434\u043d\u043e\u0439 \u0434\u0438\u0430\u0433\u0440\u0430\u043c\u043c\u044b \u0440\u0430\u0441\u0441\u0435\u044f\u043d\u0438\u044f: \u043c\u043e\u0434\u0435\u043b\u044c \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u043b\u0443\u0447\u0448\u0435 \u0432\u0441\u0435\u0433\u043e \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u0434\u0430\u043d\u043d\u044b\u043c.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">\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<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">\u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u044d\u0444\u0444\u0435\u043a\u0442\u0438\u0432\u043d\u043e\u0439 \u043c\u043e\u0434\u0435\u043b\u0438:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#fit best model<\/span>\nbest = <span style=\"color: #3366ff;\">lm<\/span> (score ~ <span style=\"color: #3366ff;\">poly<\/span> (hours,2, raw= <span style=\"color: #008000;\">T<\/span> ), data=df)\n\n<span style=\"color: #008080;\">#view summary of best model<\/span>\nsummary(best)\n\nCall:\nlm(formula = score ~ poly(hours, 2, raw = T), data = df)\n\nResiduals:\n    Min 1Q Median 3Q Max \n-5.6589 -2.0770 -0.4599 2.5923 4.5122 \n\nCoefficients:\n                         Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) 54.00526 5.52855 9.768 6.78e-13 ***\npoly(hours, 2, raw = T)1 -0.07904 1.15413 -0.068 0.94569    \npoly(hours, 2, raw = T)2 0.18596 0.05724 3.249 0.00214 ** \n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u0418\u0437 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0430 \u043c\u044b \u0432\u0438\u0434\u0438\u043c, \u0447\u0442\u043e \u043e\u043a\u043e\u043d\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u0430\u044f \u043f\u043e\u0434\u043e\u0431\u0440\u0430\u043d\u043d\u0430\u044f \u043c\u043e\u0434\u0435\u043b\u044c:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u041e\u0446\u0435\u043d\u043a\u0430 = 54,00526 \u2013 0,07904*(\u0447\u0430\u0441\u044b) + 0,18596*(\u0447\u0430\u0441\u044b) <sup>2<\/sup><\/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 \u044d\u0442\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0434\u043b\u044f \u043e\u0446\u0435\u043d\u043a\u0438 \u043e\u0446\u0435\u043d\u043a\u0438, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043f\u043e\u043b\u0443\u0447\u0438\u0442 \u0441\u0442\u0443\u0434\u0435\u043d\u0442 \u0432 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u043e\u0442 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u0430 \u0438\u0437\u0443\u0447\u0435\u043d\u043d\u044b\u0445 \u0447\u0430\u0441\u043e\u0432.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0441\u0442\u0443\u0434\u0435\u043d\u0442, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0443\u0447\u0438\u0442\u0441\u044f 10 \u0447\u0430\u0441\u043e\u0432, \u0434\u043e\u043b\u0436\u0435\u043d \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u043e\u0446\u0435\u043d\u043a\u0443 <strong>71,81<\/strong> :<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u041e\u0446\u0435\u043d\u043a\u0430 = 54,00526 \u2013 0,07904*(10) + 0,18596*(10) <sup>2<\/sup> = 71,81<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u041c\u044b \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u0435\u043c \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u0442\u044c \u043f\u043e\u0434\u043e\u0431\u0440\u0430\u043d\u043d\u0443\u044e \u043c\u043e\u0434\u0435\u043b\u044c, \u0447\u0442\u043e\u0431\u044b \u0443\u0432\u0438\u0434\u0435\u0442\u044c, \u043d\u0430\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0445\u043e\u0440\u043e\u0448\u043e \u043e\u043d\u0430 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u043d\u0435\u043e\u0431\u0440\u0430\u0431\u043e\u0442\u0430\u043d\u043d\u044b\u043c \u0434\u0430\u043d\u043d\u044b\u043c:<\/span> <\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong>ggplot(df, <span style=\"color: #3366ff;\">aes<\/span> (x=hours, y=score)) + \n          geom_point() +\n          stat_smooth(method=' <span style=\"color: #008000;\">lm<\/span> ', formula = y ~ <span style=\"color: #3366ff;\">poly<\/span> (x,2), size = 1) + \n          xlab(' <span style=\"color: #008000;\">Hours Studied<\/span> ') +\n          ylab(' <span style=\"color: #008000;\">Score<\/span> ')<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12002 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/poly2.png\" alt=\"\u041f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f \u0432 R\" width=\"446\" height=\"449\" srcset=\"\" sizes=\"auto, \"><\/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\/polynomial_regression.R\" target=\"_blank\" rel=\"noopener noreferrer\">\u0437\u0434\u0435\u0441\u044c<\/a> .<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u041f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \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, \u043a\u043e\u0433\u0434\u0430 \u0441\u0432\u044f\u0437\u044c \u043c\u0435\u0436\u0434\u0443 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439-\u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u043e\u043c \u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u043e\u0442\u0432\u0435\u0442\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0435\u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439. \u042d\u0442\u043e\u0442 \u0442\u0438\u043f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u043f\u0440\u0438\u043d\u0438\u043c\u0430\u0435\u0442 \u0444\u043e\u0440\u043c\u0443: Y = \u03b2 0 + \u03b2 1 X + \u03b2 2 X 2 + \u2026 + \u03b2 h \u0433\u0434\u0435 h \u2014 \u00ab\u0441\u0442\u0435\u043f\u0435\u043d\u044c\u00bb \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430. \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 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 [&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-473","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>\u041f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044f \u0432 R (\u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c) - Statorials<\/title>\n<meta name=\"description\" content=\"\u042d\u0442\u043e \u0440\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e 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