{"id":680,"date":"2023-07-29T02:38:21","date_gmt":"2023-07-29T02:38:21","guid":{"rendered":"https:\/\/statorials.org\/uk\/%d0%b4%d1%96%d0%b0%d0%b3%d1%80%d0%b0%d0%bc%d0%b0-%d1%80%d0%be%d0%b7%d1%81%d1%96%d1%8e%d0%b2%d0%b0%d0%bd%d0%bd%d1%8f-%d0%b7-%d0%bb%d1%96%d0%bd%d1%96%d1%94%d1%8e-%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81\/"},"modified":"2023-07-29T02:38:21","modified_gmt":"2023-07-29T02:38:21","slug":"%d0%b4%d1%96%d0%b0%d0%b3%d1%80%d0%b0%d0%bc%d0%b0-%d1%80%d0%be%d0%b7%d1%81%d1%96%d1%8e%d0%b2%d0%b0%d0%bd%d0%bd%d1%8f-%d0%b7-%d0%bb%d1%96%d0%bd%d1%96%d1%94%d1%8e-%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81","status":"publish","type":"post","link":"https:\/\/statorials.org\/uk\/%d0%b4%d1%96%d0%b0%d0%b3%d1%80%d0%b0%d0%bc%d0%b0-%d1%80%d0%be%d0%b7%d1%81%d1%96%d1%8e%d0%b2%d0%b0%d0%bd%d0%bd%d1%8f-%d0%b7-%d0%bb%d1%96%d0%bd%d1%96%d1%94%d1%8e-%d1%80%d0%b5%d0%b3%d1%80%d0%b5%d1%81\/","title":{"rendered":"\u042f\u043a \u0441\u0442\u0432\u043e\u0440\u0438\u0442\u0438 \u0434\u0456\u0430\u0433\u0440\u0430\u043c\u0443 \u0440\u043e\u0437\u0441\u0456\u044e\u0432\u0430\u043d\u043d\u044f \u0437 \u043b\u0456\u043d\u0456\u0454\u044e \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457 \u0432 r"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0427\u0430\u0441\u0442\u043e, \u043a\u043e\u043b\u0438 \u043c\u0438 \u0432\u0438\u043a\u043e\u043d\u0443\u0454\u043c\u043e \u043f\u0440\u043e\u0441\u0442\u0443 \u043b\u0456\u043d\u0456\u0439\u043d\u0443 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u044e, \u043c\u0438 \u0445\u043e\u0447\u0435\u043c\u043e \u0441\u0442\u0432\u043e\u0440\u0438\u0442\u0438 \u0434\u0456\u0430\u0433\u0440\u0430\u043c\u0443 \u0440\u043e\u0437\u0441\u0456\u044e\u0432\u0430\u043d\u043d\u044f, \u0449\u043e\u0431 \u0432\u0456\u0437\u0443\u0430\u043b\u0456\u0437\u0443\u0432\u0430\u0442\u0438 \u0440\u0456\u0437\u043d\u0456 \u043a\u043e\u043c\u0431\u0456\u043d\u0430\u0446\u0456\u0457 \u0437\u043d\u0430\u0447\u0435\u043d\u044c x \u0456 y.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u041d\u0430 \u0449\u0430\u0441\u0442\u044f, R \u0434\u043e\u0437\u0432\u043e\u043b\u044f\u0454 \u043b\u0435\u0433\u043a\u043e \u0441\u0442\u0432\u043e\u0440\u044e\u0432\u0430\u0442\u0438 \u0445\u043c\u0430\u0440\u0438 \u0442\u043e\u0447\u043e\u043a \u0437\u0430 \u0434\u043e\u043f\u043e\u043c\u043e\u0433\u043e\u044e \u0444\u0443\u043d\u043a\u0446\u0456\u0457 <strong>plot()<\/strong> . \u041d\u0430\u043f\u0440\u0438\u043a\u043b\u0430\u0434:<\/span> <\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create some fake data<\/span>\ndata &lt;- data.frame(x = c(1, 1, 2, 3, 4, 4, 5, 6, 7, 7, 8, 9, 10, 11, 11),\n                   y = c(13, 14, 17, 12, 23, 24, 25, 25, 24, 28, 32, 33, 35, 40, 41))\n\n<span style=\"color: #008080;\">#create scatterplot of data<\/span>\nplot(data$x, data$y)\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-6570 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/scatterregression1.png\" alt=\"\u0414\u0456\u0430\u0433\u0440\u0430\u043c\u0430 \u0440\u043e\u0437\u0441\u0456\u044e\u0432\u0430\u043d\u043d\u044f \u0432 R\" width=\"434\" height=\"396\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">\u0422\u0430\u043a\u043e\u0436 \u043b\u0435\u0433\u043a\u043e \u0434\u043e\u0434\u0430\u0442\u0438 \u043b\u0456\u043d\u0456\u044e \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457 \u0434\u043e \u0434\u0456\u0430\u0433\u0440\u0430\u043c\u0438 \u0440\u043e\u0437\u0441\u0456\u044e\u0432\u0430\u043d\u043d\u044f \u0437\u0430 \u0434\u043e\u043f\u043e\u043c\u043e\u0433\u043e\u044e \u0444\u0443\u043d\u043a\u0446\u0456\u0457 <strong>abline()<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u041d\u0430\u043f\u0440\u0438\u043a\u043b\u0430\u0434:<\/span> <\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#fit a simple linear regression model<\/span>\nmodel &lt;- lm(y ~ x, data = data)\n\n<span style=\"color: #008080;\">#add the fitted regression line to the scatterplot<\/span>\nabline(model)<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-6571 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/scatterregression2.png\" alt=\"\u0414\u0456\u0430\u0433\u0440\u0430\u043c\u0430 \u0440\u043e\u0437\u0441\u0456\u044e\u0432\u0430\u043d\u043d\u044f \u0437 \u043b\u0456\u043d\u0456\u0454\u044e \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457 \u0432 R\" width=\"438\" height=\"394\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">\u041c\u0438 \u0442\u0430\u043a\u043e\u0436 \u043c\u043e\u0436\u0435\u043c\u043e \u0434\u043e\u0434\u0430\u0442\u0438 \u043b\u0456\u043d\u0456\u0457 \u0434\u043e\u0432\u0456\u0440\u0447\u043e\u0433\u043e \u0456\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0443 \u0434\u043e \u0433\u0440\u0430\u0444\u0456\u043a\u0430 \u0437\u0430 \u0434\u043e\u043f\u043e\u043c\u043e\u0433\u043e\u044e \u0444\u0443\u043d\u043a\u0446\u0456\u0457 <strong>predict()<\/strong> :<\/span> <\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define range of x values<\/span>\nnewx = seq(min(data$x),max(data$x),by = 1)\n<span style=\"color: #008080;\">\n#find 95% confidence interval for the range of x values<\/span> \nconf_interval &lt;- predict(model, newdata=data.frame(x=newx), interval=\"confidence\",\n                         level = 0.95)\n<span style=\"color: #008080;\">\n#create scatterplot of values with regression line<\/span>\nplot(data$x, data$y)\nabline(model)\n\n<span style=\"color: #008080;\">#add dashed lines (lty=2) for the 95% confidence interval<\/span>\nlines(newx, conf_interval[,2], col=\"blue\", lty=2)\nlines(newx, conf_interval[,3], col=\"blue\", lty=2)\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-6573 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/scatterregression3.png\" alt=\"\u041b\u0456\u043d\u0456\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457 \u0437 \u0434\u043e\u0432\u0456\u0440\u0447\u0438\u043c \u0456\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u043e\u043c \u0432 R\" width=\"430\" height=\"396\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">\u0410\u0431\u043e \u0437\u0430\u043c\u0456\u0441\u0442\u044c \u0446\u044c\u043e\u0433\u043e \u043c\u0438 \u043c\u043e\u0433\u043b\u0438 \u0431 \u0434\u043e\u0434\u0430\u0442\u0438 \u043b\u0456\u043d\u0456\u0457 \u0456\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0443 \u043f\u0435\u0440\u0435\u0434\u0431\u0430\u0447\u0435\u043d\u043d\u044f \u043d\u0430 \u0433\u0440\u0430\u0444\u0456\u043a, \u0432\u043a\u0430\u0437\u0430\u0432\u0448\u0438 \u0442\u0438\u043f \u0456\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0443 \u0443 \u0444\u0443\u043d\u043a\u0446\u0456\u0457 <strong>predict()<\/strong> :<\/span> <\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define range of x values<\/span>\nnewx = seq(min(data$x),max(data$x),by = 1)\n<span style=\"color: #008080;\">\n#find 95% prediction interval for the range of x values<\/span> \npred_interval &lt;- predict(model, newdata=data.frame(x=newx), <span style=\"color: #993366;\">interval=\"prediction\"<\/span> ,\n                         level = 0.95)\n<span style=\"color: #008080;\">\n#create scatterplot of values with regression line<\/span>\nplot(data$x, data$y)\nabline(model)\n\n<span style=\"color: #008080;\">#add dashed lines (lty=2) for the 95% confidence interval<\/span>\nlines(newx, pred_interval[,2], col=\"red\", lty=2)\nlines(newx, pred_interval[,3], col=\"red\", lty=2)\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-6574\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/scatterregression4.png\" alt=\"\u041b\u0456\u043d\u0456\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457 \u0437 \u043b\u0456\u043d\u0456\u044f\u043c\u0438 \u0456\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0443 \u043f\u0435\u0440\u0435\u0434\u0431\u0430\u0447\u0435\u043d\u043d\u044f \u0432 R\" width=\"432\" height=\"394\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">\u041d\u0430\u0440\u0435\u0448\u0442\u0456, \u043c\u0438 \u043c\u043e\u0436\u0435\u043c\u043e \u0437\u0440\u043e\u0431\u0438\u0442\u0438 \u0441\u044e\u0436\u0435\u0442 \u0431\u0456\u043b\u044c\u0448 \u0435\u0441\u0442\u0435\u0442\u0438\u0447\u043d\u043e \u043f\u0440\u0438\u0432\u0430\u0431\u043b\u0438\u0432\u0438\u043c, \u0434\u043e\u0434\u0430\u0432\u0448\u0438 \u043d\u0430\u0437\u0432\u0443, \u0437\u043c\u0456\u043d\u0438\u0432\u0448\u0438 \u043d\u0430\u0437\u0432\u0438 \u043e\u0441\u0435\u0439 \u0456 \u0437\u043c\u0456\u043d\u0438\u0432\u0448\u0438 \u0444\u043e\u0440\u043c\u0443 \u043e\u043a\u0440\u0435\u043c\u0438\u0445 \u0442\u043e\u0447\u043e\u043a \u0433\u0440\u0430\u0444\u0456\u043a\u0430.<\/span> <\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong>plot(data$x, data$y,\n     main = \"Scatterplot of x vs. y\", <span style=\"color: #008080;\">#add title<\/span>\n     pch=16, <span style=\"color: #008080;\">#specify points to be filled in<\/span>\n     xlab='x', <span style=\"color: #008080;\">#change x-axis name\n<\/span>ylab='y') <span style=\"color: #008080;\">#change y-axis name<\/span>\n\nabline(model, col='steelblue') <span style=\"color: #008080;\"><span style=\"color: #008080;\">#specify color of regression line<\/span><\/span>\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-6576 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/scatterregression5.png\" alt=\"\u041b\u0456\u043d\u0456\u044f \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457 \u0437 \u0434\u0456\u0430\u0433\u0440\u0430\u043c\u043e\u044e \u0440\u043e\u0437\u0441\u0456\u044e\u0432\u0430\u043d\u043d\u044f \u0432 R\" width=\"432\" height=\"417\" srcset=\"\" sizes=\"\"><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u0414\u043e\u0434\u0430\u0442\u043a\u043e\u0432\u0456 \u0440\u0435\u0441\u0443\u0440\u0441\u0438<\/strong><\/span><\/h2>\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 \u0437\u0430\u0432\u0434\u0430\u043d\u043d\u044f \u0432 R:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/uk\/\u0445\u043c\u0430\u0440\u0430-\u0442\u043e\u0447\u043e\u043a-\u043c\u0456\u0442\u043a\u0438-r\/\" target=\"_blank\" rel=\"noopener\">\u042f\u043a \u043f\u043e\u0437\u043d\u0430\u0447\u0438\u0442\u0438 \u0442\u043e\u0447\u043a\u0438 \u043d\u0430 \u0434\u0456\u0430\u0433\u0440\u0430\u043c\u0456 \u0440\u043e\u0437\u0441\u0456\u044e\u0432\u0430\u043d\u043d\u044f \u0432 R<\/a><br \/> <a href=\"https:\/\/statorials.org\/uk\/\u0444\u0443\u043d\u043a\u0446\u0456\u044f-\u0442\u0440\u0435\u043c\u0442\u0456\u043d\u043d\u044f-r\/\" target=\"_blank\" rel=\"noopener\">\u042f\u043a \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0456\u044e \u0434\u0436\u0438\u0442\u0442\u0435\u0440\u0430 \u0432 R \u0434\u043b\u044f \u0445\u043c\u0430\u0440 \u0442\u043e\u0447\u043e\u043a<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0427\u0430\u0441\u0442\u043e, \u043a\u043e\u043b\u0438 \u043c\u0438 \u0432\u0438\u043a\u043e\u043d\u0443\u0454\u043c\u043e \u043f\u0440\u043e\u0441\u0442\u0443 \u043b\u0456\u043d\u0456\u0439\u043d\u0443 \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u044e, \u043c\u0438 \u0445\u043e\u0447\u0435\u043c\u043e \u0441\u0442\u0432\u043e\u0440\u0438\u0442\u0438 \u0434\u0456\u0430\u0433\u0440\u0430\u043c\u0443 \u0440\u043e\u0437\u0441\u0456\u044e\u0432\u0430\u043d\u043d\u044f, \u0449\u043e\u0431 \u0432\u0456\u0437\u0443\u0430\u043b\u0456\u0437\u0443\u0432\u0430\u0442\u0438 \u0440\u0456\u0437\u043d\u0456 \u043a\u043e\u043c\u0431\u0456\u043d\u0430\u0446\u0456\u0457 \u0437\u043d\u0430\u0447\u0435\u043d\u044c x \u0456 y. \u041d\u0430 \u0449\u0430\u0441\u0442\u044f, R \u0434\u043e\u0437\u0432\u043e\u043b\u044f\u0454 \u043b\u0435\u0433\u043a\u043e \u0441\u0442\u0432\u043e\u0440\u044e\u0432\u0430\u0442\u0438 \u0445\u043c\u0430\u0440\u0438 \u0442\u043e\u0447\u043e\u043a \u0437\u0430 \u0434\u043e\u043f\u043e\u043c\u043e\u0433\u043e\u044e \u0444\u0443\u043d\u043a\u0446\u0456\u0457 plot() . \u041d\u0430\u043f\u0440\u0438\u043a\u043b\u0430\u0434: #create some fake data data &lt;- data.frame(x = c(1, 1, 2, 3, 4, 4, 5, 6, 7, 7, 8, 9, 10, [&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 \u0441\u0442\u0432\u043e\u0440\u0438\u0442\u0438 \u0442\u043e\u0447\u043a\u043e\u0432\u0443 \u0434\u0456\u0430\u0433\u0440\u0430\u043c\u0443 \u0437 \u043b\u0456\u043d\u0456\u0454\u044e \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u0457 \u0432 R - Statology<\/title>\n<meta name=\"description\" content=\"\u041f\u0440\u043e\u0441\u0442\u0435 \u043f\u043e\u044f\u0441\u043d\u0435\u043d\u043d\u044f \u0442\u043e\u0433\u043e, \u044f\u043a \u0441\u0442\u0432\u043e\u0440\u0438\u0442\u0438 \u0434\u0456\u0430\u0433\u0440\u0430\u043c\u0443 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