{"id":3011,"date":"2023-07-19T15:30:27","date_gmt":"2023-07-19T15:30:27","guid":{"rendered":"https:\/\/statorials.org\/uk\/%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d1%96%d1%8f-%d0%b2-r\/"},"modified":"2023-07-19T15:30:27","modified_gmt":"2023-07-19T15:30:27","slug":"%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d1%96%d1%8f-%d0%b2-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/uk\/%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d1%96%d1%8f-%d0%b2-r\/","title":{"rendered":"\u042f\u043a \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0456\u044e optim \u0443 r (2 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u0438)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0412\u0438 \u043c\u043e\u0436\u0435\u0442\u0435 \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0456\u044e <strong>optim<\/strong> \u0443 R \u0434\u043b\u044f \u0437\u0430\u0433\u0430\u043b\u044c\u043d\u043e\u0457 \u043e\u043f\u0442\u0438\u043c\u0456\u0437\u0430\u0446\u0456\u0457.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0426\u044f \u0444\u0443\u043d\u043a\u0446\u0456\u044f \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0454 \u0442\u0430\u043a\u0438\u0439 \u0431\u0430\u0437\u043e\u0432\u0438\u0439 \u0441\u0438\u043d\u0442\u0430\u043a\u0441\u0438\u0441:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong>optim(by, fn, data, ...)\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u0437\u043e\u043b\u043e\u0442\u043e:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>by<\/strong> : \u041f\u043e\u0447\u0430\u0442\u043a\u043e\u0432\u0456 \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0456\u0432, \u044f\u043a\u0456 \u0431\u0443\u0434\u0443\u0442\u044c \u043e\u043f\u0442\u0438\u043c\u0456\u0437\u043e\u0432\u0430\u043d\u0456<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>fn<\/strong> : \u0444\u0443\u043d\u043a\u0446\u0456\u044f \u0434\u043b\u044f \u043c\u0456\u043d\u0456\u043c\u0456\u0437\u0430\u0446\u0456\u0457 \u0430\u0431\u043e \u0440\u043e\u0437\u0433\u043e\u0440\u0442\u0430\u043d\u043d\u044f<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>data<\/strong> : \u0456\u043c&#8217;\u044f \u043e\u0431&#8217;\u0454\u043a\u0442\u0430 \u0432 R, \u044f\u043a\u0438\u0439 \u043c\u0456\u0441\u0442\u0438\u0442\u044c \u0434\u0430\u043d\u0456<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u0423 \u043d\u0430\u0432\u0435\u0434\u0435\u043d\u0438\u0445 \u043d\u0438\u0436\u0447\u0435 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u0430\u0445 \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u043e, \u044f\u043a \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u0446\u044e \u0444\u0443\u043d\u043a\u0446\u0456\u044e \u0432 \u0442\u0430\u043a\u0438\u0445 \u0441\u0446\u0435\u043d\u0430\u0440\u0456\u044f\u0445:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> \u0417\u043d\u0430\u0439\u0442\u0438 \u043a\u043e\u0435\u0444\u0456\u0446\u0456\u0454\u043d\u0442\u0438 \u043c\u043e\u0434\u0435\u043b\u0456 \u043b\u0456\u043d\u0456\u0439\u043d\u043e\u0457 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2.<\/strong> \u0417\u043d\u0430\u0439\u0442\u0438 \u043a\u043e\u0435\u0444\u0456\u0446\u0456\u0454\u043d\u0442\u0438 \u043c\u043e\u0434\u0435\u043b\u0456 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u043e\u0457 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0425\u043e\u0434\u0456\u043c\u043e!<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u041f\u0440\u0438\u043a\u043b\u0430\u0434 1: \u0432\u0438\u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u043a\u043e\u0435\u0444\u0456\u0446\u0456\u0454\u043d\u0442\u0456\u0432 \u0434\u043b\u044f \u043c\u043e\u0434\u0435\u043b\u0456 \u043b\u0456\u043d\u0456\u0439\u043d\u043e\u0457 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0423 \u043d\u0430\u0441\u0442\u0443\u043f\u043d\u043e\u043c\u0443 \u043a\u043e\u0434\u0456 \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u043e, \u044f\u043a \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0456\u044e <strong>optim()<\/strong> \u0434\u043b\u044f \u0437\u043d\u0430\u0445\u043e\u0434\u0436\u0435\u043d\u043d\u044f \u043a\u043e\u0435\u0444\u0456\u0446\u0456\u0454\u043d\u0442\u0456\u0432 \u043c\u043e\u0434\u0435\u043b\u0456 \u043b\u0456\u043d\u0456\u0439\u043d\u043e\u0457 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457 \u0448\u043b\u044f\u0445\u043e\u043c \u043c\u0456\u043d\u0456\u043c\u0456\u0437\u0430\u0446\u0456\u0457 \u0437\u0430\u043b\u0438\u0448\u043a\u043e\u0432\u043e\u0457 \u0441\u0443\u043c\u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0456\u0432:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008080;\">#create data frame\n<\/span>df &lt;- data.frame(x=c(1, 3, 3, 5, 6, 7, 9, 12),\n                 y=c(4, 5, 8, 6, 9, 10, 13, 17))\n\n<span style=\"color: #008080;\">#define function to minimize residual sum of squares\n<\/span>min_residuals &lt;- <span style=\"color: #008000;\">function<\/span> (data, par) {\n                   <span style=\"color: #008000;\">with<\/span> (data, sum((par[1] + par[2] * x - y)^2))\n}\n\n<span style=\"color: #008080;\">#find coefficients of linear regression model\n<\/span>optim(par=c(0, 1), fn=min_residuals, data=df)\n\n$by\n[1] 2.318592 1.162012\n\n$value\n[1] 11.15084\n\n$counts\nfunction gradient \n      79 NA \n\n$convergence\n[1] 0\n\n$message\nNULL\n<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u0412\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u044e\u0447\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f, \u043f\u043e\u0432\u0435\u0440\u043d\u0435\u043d\u0456 \u0432 <strong>$par<\/strong> , \u043c\u0438 \u043c\u043e\u0436\u0435\u043c\u043e \u043d\u0430\u043f\u0438\u0441\u0430\u0442\u0438 \u043d\u0430\u0441\u0442\u0443\u043f\u043d\u0443 \u043c\u043e\u0434\u0435\u043b\u044c \u043b\u0456\u043d\u0456\u0439\u043d\u043e\u0457 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457:<\/span><\/p>\n<p> <span style=\"color: #000000;\">y = 2,318 + 1,162x<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u041c\u0438 \u043c\u043e\u0436\u0435\u043c\u043e \u043f\u0435\u0440\u0435\u043a\u043e\u043d\u0430\u0442\u0438\u0441\u044f, \u0449\u043e \u0446\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e, \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u044e\u0447\u0438 \u0432\u0431\u0443\u0434\u043e\u0432\u0430\u043d\u0443 \u0444\u0443\u043d\u043a\u0446\u0456\u044e <strong>lm()<\/strong> \u0443 R \u0434\u043b\u044f \u043e\u0431\u0447\u0438\u0441\u043b\u0435\u043d\u043d\u044f \u043a\u043e\u0435\u0444\u0456\u0446\u0456\u0454\u043d\u0442\u0456\u0432 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#find coefficients of linear regression model using lm() function\n<span style=\"color: #000000;\">lm(y ~ x, data=df)\n\nCall:\nlm(formula = y ~ x, data = df)\n\nCoefficients:\n(Intercept) x  \n      2,318 1,162\n<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u0426\u0456 \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u043a\u043e\u0435\u0444\u0456\u0446\u0456\u0454\u043d\u0442\u0456\u0432 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0430\u044e\u0442\u044c \u0442\u0438\u043c, \u044f\u043a\u0456 \u043c\u0438 \u0440\u043e\u0437\u0440\u0430\u0445\u0443\u0432\u0430\u043b\u0438 \u0437\u0430 \u0434\u043e\u043f\u043e\u043c\u043e\u0433\u043e\u044e \u0444\u0443\u043d\u043a\u0446\u0456\u0457 <strong>optim()<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u041f\u0440\u0438\u043a\u043b\u0430\u0434 2: \u0432\u0438\u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u043a\u043e\u0435\u0444\u0456\u0446\u0456\u0454\u043d\u0442\u0456\u0432 \u0434\u043b\u044f \u043c\u043e\u0434\u0435\u043b\u0456 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u043e\u0457 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0423 \u043d\u0430\u0441\u0442\u0443\u043f\u043d\u043e\u043c\u0443 \u043a\u043e\u0434\u0456 \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u043e, \u044f\u043a \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0456\u044e <strong>optim()<\/strong> \u0434\u043b\u044f \u0437\u043d\u0430\u0445\u043e\u0434\u0436\u0435\u043d\u043d\u044f \u043a\u043e\u0435\u0444\u0456\u0446\u0456\u0454\u043d\u0442\u0456\u0432 <a href=\"https:\/\/statorials.org\/uk\/\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u0430-\u0440\u0435\u0433\u0440\u0435\u0441\u0456\u044f-r\/\" target=\"_blank\" rel=\"noopener\">\u043c\u043e\u0434\u0435\u043b\u0456 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u043e\u0457 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457<\/a> \u0448\u043b\u044f\u0445\u043e\u043c \u043c\u0456\u043d\u0456\u043c\u0456\u0437\u0430\u0446\u0456\u0457 \u0437\u0430\u043b\u0438\u0448\u043a\u043e\u0432\u043e\u0457 \u0441\u0443\u043c\u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0456\u0432:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008080;\">#create data frame<\/span>\ndf &lt;- data. <span style=\"color: #3366ff;\">frame<\/span> (x=c(6, 9, 12, 14, 30, 35, 40, 47, 51, 55, 60),\n                 y=c(14, 28, 50, 70, 89, 94, 90, 75, 59, 44, 27))<\/span>\n\n<span style=\"color: #000000;\"><span style=\"color: #008080;\">#define function to minimize residual sum of squares\n<\/span>min_residuals &lt;- <span style=\"color: #008000;\">function<\/span> (data, par) {\n                   <span style=\"color: #008000;\">with<\/span> (data, sum((par[1] + par[2]*x + par[3]*x^2 - y)^2))\n}\n\n<span style=\"color: #008080;\">#find coefficients of quadratic regression model\n<\/span>optim(par=c(0, 0, 0), fn=min_residuals, data=df)\n\n$by\n[1] -18.261320 6.744531 -0.101201\n\n$value\n[1] 309.3412\n\n$counts\nfunction gradient \n     218 NA \n\n$convergence\n[1] 0\n\n$message\nNULL<\/span><\/span><\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u0412\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u044e\u0447\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f, \u043f\u043e\u0432\u0435\u0440\u043d\u0435\u043d\u0456 \u0432 <strong>$par<\/strong> , \u043c\u0438 \u043c\u043e\u0436\u0435\u043c\u043e \u043d\u0430\u043f\u0438\u0441\u0430\u0442\u0438 \u0442\u0430\u043a\u0443 \u043f\u0456\u0434\u0456\u0433\u043d\u0430\u043d\u0443 \u043c\u043e\u0434\u0435\u043b\u044c \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u043e\u0457 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457:<\/span><\/p>\n<p> <span style=\"color: #000000;\">y = -18,261 + 6,744x \u2013 0,101x <sup>2<\/sup><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u041c\u0438 \u043c\u043e\u0436\u0435\u043c\u043e \u043f\u0435\u0440\u0435\u0432\u0456\u0440\u0438\u0442\u0438, \u0449\u043e \u0446\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e, \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u044e\u0447\u0438 \u0432\u0431\u0443\u0434\u043e\u0432\u0430\u043d\u0443 \u0444\u0443\u043d\u043a\u0446\u0456\u044e <strong>lm()<\/strong> \u0443 R:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008080;\">#create data frame\n<\/span>df &lt;- data. <span style=\"color: #3366ff;\">frame<\/span> (x=c(6, 9, 12, 14, 30, 35, 40, 47, 51, 55, 60),\n                 y=c(14, 28, 50, 70, 89, 94, 90, 75, 59, 44, 27))\n\n<span style=\"color: #008080;\">#create a new variable for x^2\n<\/span>df$x2 &lt;- df$x^2\n\n<span style=\"color: #008080;\">#fit quadratic regression model\n<\/span>quadraticModel &lt;- lm(y ~ x + x2, data=df)\n\n<span style=\"color: #008080;\">#display coefficients of quadratic regression model\n<\/span>summary(quadraticModel)$coef\n\n               Estimate Std. Error t value Pr(&gt;|t|)\n(Intercept) -18.2536400 6.185069026 -2.951243 1.839072e-02\nx 6.7443581 0.485515334 13.891133 6.978849e-07\nx2 -0.1011996 0.007460089 -13.565470 8.378822e-07<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u0426\u0456 \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u043a\u043e\u0435\u0444\u0456\u0446\u0456\u0454\u043d\u0442\u0456\u0432 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0430\u044e\u0442\u044c \u0442\u0438\u043c, \u044f\u043a\u0456 \u043c\u0438 \u0440\u043e\u0437\u0440\u0430\u0445\u0443\u0432\u0430\u043b\u0438 \u0437\u0430 \u0434\u043e\u043f\u043e\u043c\u043e\u0433\u043e\u044e \u0444\u0443\u043d\u043a\u0446\u0456\u0457 <strong>optim()<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u0414\u043e\u0434\u0430\u0442\u043a\u043e\u0432\u0456 \u0440\u0435\u0441\u0443\u0440\u0441\u0438<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0423 \u043d\u0430\u0441\u0442\u0443\u043f\u043d\u0438\u0445 \u043f\u043e\u0441\u0456\u0431\u043d\u0438\u043a\u0430\u0445 \u043f\u043e\u044f\u0441\u043d\u044e\u0454\u0442\u044c\u0441\u044f, \u044f\u043a \u0432\u0438\u043a\u043e\u043d\u0443\u0432\u0430\u0442\u0438 \u0456\u043d\u0448\u0456 \u0442\u0438\u043f\u043e\u0432\u0456 \u043e\u043f\u0435\u0440\u0430\u0446\u0456\u0457 \u0432 R:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/uk\/\u043f\u0440\u043e\u0441\u0442\u0430-\u043b\u0456\u043d\u0456\u0438\u043d\u0430-\u0440\u0435\u0433\u0440\u0435\u0441\u0456\u044f-\u043f\u043e-r\/\" target=\"_blank\" rel=\"noopener\">\u042f\u043a \u0432\u0438\u043a\u043e\u043d\u0430\u0442\u0438 \u043f\u0440\u043e\u0441\u0442\u0443 \u043b\u0456\u043d\u0456\u0439\u043d\u0443 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u044e \u0432 R<\/a><br \/> <a href=\"https:\/\/statorials.org\/uk\/\u043c\u043d\u043e\u0436\u0438\u043d\u043d\u0430-\u043b\u0456\u043d\u0456\u0438\u043d\u0430-\u0440\u0435\u0433\u0440\u0435\u0441\u0456\u044f-r\/\" target=\"_blank\" rel=\"noopener\">\u042f\u043a \u0432\u0438\u043a\u043e\u043d\u0430\u0442\u0438 \u043c\u043d\u043e\u0436\u0438\u043d\u043d\u0443 \u043b\u0456\u043d\u0456\u0439\u043d\u0443 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u044e \u0432 R<\/a><br \/> <a href=\"https:\/\/statorials.org\/uk\/\u0456\u043d\u0442\u0435\u0440\u043f\u0440\u0435\u0442\u0443\u0432\u0430\u0442\u0438-\u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442-\u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0456-\u0432-r\/\" target=\"_blank\" rel=\"noopener\">\u042f\u043a \u0456\u043d\u0442\u0435\u0440\u043f\u0440\u0435\u0442\u0443\u0432\u0430\u0442\u0438 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457 \u0432 R<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0412\u0438 \u043c\u043e\u0436\u0435\u0442\u0435 \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0456\u044e optim \u0443 R \u0434\u043b\u044f \u0437\u0430\u0433\u0430\u043b\u044c\u043d\u043e\u0457 \u043e\u043f\u0442\u0438\u043c\u0456\u0437\u0430\u0446\u0456\u0457. \u0426\u044f \u0444\u0443\u043d\u043a\u0446\u0456\u044f \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0454 \u0442\u0430\u043a\u0438\u0439 \u0431\u0430\u0437\u043e\u0432\u0438\u0439 \u0441\u0438\u043d\u0442\u0430\u043a\u0441\u0438\u0441: optim(by, fn, data, &#8230;) \u0437\u043e\u043b\u043e\u0442\u043e: by : \u041f\u043e\u0447\u0430\u0442\u043a\u043e\u0432\u0456 \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0456\u0432, \u044f\u043a\u0456 \u0431\u0443\u0434\u0443\u0442\u044c \u043e\u043f\u0442\u0438\u043c\u0456\u0437\u043e\u0432\u0430\u043d\u0456 fn : \u0444\u0443\u043d\u043a\u0446\u0456\u044f \u0434\u043b\u044f \u043c\u0456\u043d\u0456\u043c\u0456\u0437\u0430\u0446\u0456\u0457 \u0430\u0431\u043e \u0440\u043e\u0437\u0433\u043e\u0440\u0442\u0430\u043d\u043d\u044f data : \u0456\u043c&#8217;\u044f \u043e\u0431&#8217;\u0454\u043a\u0442\u0430 \u0432 R, \u044f\u043a\u0438\u0439 \u043c\u0456\u0441\u0442\u0438\u0442\u044c \u0434\u0430\u043d\u0456 \u0423 \u043d\u0430\u0432\u0435\u0434\u0435\u043d\u0438\u0445 \u043d\u0438\u0436\u0447\u0435 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u0430\u0445 \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u043e, \u044f\u043a \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u0446\u044e \u0444\u0443\u043d\u043a\u0446\u0456\u044e \u0432 [&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>\u042f\u043a \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0456\u044e optim \u0432 R (2 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u0438) - \u0421\u0442\u0430\u0442\u043e\u0440\u0456\u0430\u043b\u0438<\/title>\n<meta name=\"description\" content=\"\u0423 \u0446\u044c\u043e\u043c\u0443 \u043f\u0456\u0434\u0440\u0443\u0447\u043d\u0438\u043a\u0443 \u043f\u043e\u044f\u0441\u043d\u044e\u0454\u0442\u044c\u0441\u044f, \u044f\u043a \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0456\u044e optim() \u0443 R \u0456\u0437 \u043a\u0456\u043b\u044c\u043a\u043e\u043c\u0430 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u0430\u043c\u0438.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/uk\/\u043e\u043f\u0442\u0438\u043c\u0430\u043b\u044c\u043d\u0430-\u0444\u0443\u043d\u043a\u0446\u0456\u044f-\u0432-r\/\" \/>\n<meta property=\"og:locale\" content=\"uk_UA\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u042f\u043a \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0456\u044e optim \u0432 R (2 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u0438) - \u0421\u0442\u0430\u0442\u043e\u0440\u0456\u0430\u043b\u0438\" \/>\n<meta property=\"og:description\" content=\"\u0423 \u0446\u044c\u043e\u043c\u0443 \u043f\u0456\u0434\u0440\u0443\u0447\u043d\u0438\u043a\u0443 \u043f\u043e\u044f\u0441\u043d\u044e\u0454\u0442\u044c\u0441\u044f, \u044f\u043a \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0456\u044e optim() \u0443 R \u0456\u0437 \u043a\u0456\u043b\u044c\u043a\u043e\u043c\u0430 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u0430\u043c\u0438.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/uk\/\u043e\u043f\u0442\u0438\u043c\u0430\u043b\u044c\u043d\u0430-\u0444\u0443\u043d\u043a\u0446\u0456\u044f-\u0432-r\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-19T15:30:27+00:00\" \/>\n<meta name=\"author\" content=\"\u0420\u0435\u0434\u0430\u043a\u0446\u0456\u044f\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u041d\u0430\u043f\u0438\u0441\u0430\u043d\u043e\" \/>\n\t<meta name=\"twitter:data1\" content=\"\u0420\u0435\u0434\u0430\u043a\u0446\u0456\u044f\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u041f\u0440\u0438\u0431\u043b. \u0447\u0430\u0441 \u0447\u0438\u0442\u0430\u043d\u043d\u044f\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 \u0445\u0432\u0438\u043b\u0438\u043d\u0430\" \/>\n<script type=\"application\/ld+json\" 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\u0446\u044c\u043e\u043c\u0443 \u043f\u0456\u0434\u0440\u0443\u0447\u043d\u0438\u043a\u0443 \u043f\u043e\u044f\u0441\u043d\u044e\u0454\u0442\u044c\u0441\u044f, \u044f\u043a \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0456\u044e optim() \u0443 R \u0456\u0437 \u043a\u0456\u043b\u044c\u043a\u043e\u043c\u0430 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u0430\u043c\u0438.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/uk\/%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d1%96%d1%8f-%d0%b2-r\/#breadcrumb\"},\"inLanguage\":\"uk\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/uk\/%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d1%96%d1%8f-%d0%b2-r\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/uk\/%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d1%96%d1%8f-%d0%b2-r\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u0434\u043e\u0434\u043e\u043c\u0443\",\"item\":\"https:\/\/statorials.org\/uk\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u042f\u043a \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0456\u044e optim \u0443 r (2 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u0438)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/uk\/#website\",\"url\":\"https:\/\/statorials.org\/uk\/\",\"name\":\"Statorials\",\"description\":\"\u0412\u0430\u0448 \u043f\u0443\u0442\u0456\u0432\u043d\u0438\u043a \u0434\u043e \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u0447\u043d\u043e\u0457 \u043a\u043e\u043c\u043f\u0435\u0442\u0435\u043d\u0442\u043d\u043e\u0441\u0442\u0456!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/uk\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"uk\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/uk\/#\/schema\/person\/2affa1a5da08a4b61ab4becd078c191a\",\"name\":\"\u0420\u0435\u0434\u0430\u043a\u0446\u0456\u044f\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"uk\",\"@id\":\"https:\/\/statorials.org\/uk\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/uk\/wp-content\/uploads\/2023\/11\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/uk\/wp-content\/uploads\/2023\/11\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"\u0420\u0435\u0434\u0430\u043a\u0446\u0456\u044f\"},\"description\":\"\u041f\u0440\u0438\u0432\u0456\u0442, \u044f \u0411\u0435\u043d\u0434\u0436\u0430\u043c\u0456\u043d, \u043f\u0440\u043e\u0444\u0435\u0441\u043e\u0440 \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043a\u0438 \u043d\u0430 \u043f\u0435\u043d\u0441\u0456\u0457, \u044f\u043a\u0438\u0439 \u0441\u0442\u0430\u0432 \u0432\u0438\u043a\u043b\u0430\u0434\u0430\u0447\u0435\u043c \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043a\u0438. \u041c\u0430\u044e\u0447\u0438 \u0432\u0435\u043b\u0438\u043a\u0438\u0439 \u0434\u043e\u0441\u0432\u0456\u0434 \u0456 \u0437\u043d\u0430\u043d\u043d\u044f \u0432 \u0433\u0430\u043b\u0443\u0437\u0456 \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043a\u0438, \u044f \u0433\u043e\u0442\u043e\u0432\u0438\u0439 \u043f\u043e\u0434\u0456\u043b\u0438\u0442\u0438\u0441\u044f \u0441\u0432\u043e\u0457\u043c\u0438 \u0437\u043d\u0430\u043d\u043d\u044f\u043c\u0438, \u0449\u043e\u0431 \u0440\u043e\u0437\u0448\u0438\u0440\u0438\u0442\u0438 \u043c\u043e\u0436\u043b\u0438\u0432\u043e\u0441\u0442\u0456 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0456\u0432 \u0447\u0435\u0440\u0435\u0437 Statorials. \u0414\u0456\u0437\u043d\u0430\u0439\u0442\u0435\u0441\u044f \u0431\u0456\u043b\u044c\u0448\u0435\",\"sameAs\":[\"http:\/\/statorials.org\/uk\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u042f\u043a \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0456\u044e optim \u0432 R (2 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u0438) - \u0421\u0442\u0430\u0442\u043e\u0440\u0456\u0430\u043b\u0438","description":"\u0423 \u0446\u044c\u043e\u043c\u0443 \u043f\u0456\u0434\u0440\u0443\u0447\u043d\u0438\u043a\u0443 \u043f\u043e\u044f\u0441\u043d\u044e\u0454\u0442\u044c\u0441\u044f, \u044f\u043a \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0456\u044e optim() \u0443 R \u0456\u0437 \u043a\u0456\u043b\u044c\u043a\u043e\u043c\u0430 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