{"id":683,"date":"2023-07-29T02:38:21","date_gmt":"2023-07-29T02:38:21","guid":{"rendered":"https:\/\/statorials.org\/th\/%e0%b8%9e%e0%b8%a5%e0%b9%87%e0%b8%ad%e0%b8%95%e0%b8%81%e0%b8%a3%e0%b8%b0%e0%b8%88%e0%b8%b2%e0%b8%a2%e0%b8%94%e0%b9%89%e0%b8%a7%e0%b8%a2%e0%b9%80%e0%b8%aa%e0%b9%89%e0%b8%99%e0%b8%96%e0%b8%94%e0%b8%96\/"},"modified":"2023-07-29T02:38:21","modified_gmt":"2023-07-29T02:38:21","slug":"%e0%b8%9e%e0%b8%a5%e0%b9%87%e0%b8%ad%e0%b8%95%e0%b8%81%e0%b8%a3%e0%b8%b0%e0%b8%88%e0%b8%b2%e0%b8%a2%e0%b8%94%e0%b9%89%e0%b8%a7%e0%b8%a2%e0%b9%80%e0%b8%aa%e0%b9%89%e0%b8%99%e0%b8%96%e0%b8%94%e0%b8%96","status":"publish","type":"post","link":"https:\/\/statorials.org\/th\/%e0%b8%9e%e0%b8%a5%e0%b9%87%e0%b8%ad%e0%b8%95%e0%b8%81%e0%b8%a3%e0%b8%b0%e0%b8%88%e0%b8%b2%e0%b8%a2%e0%b8%94%e0%b9%89%e0%b8%a7%e0%b8%a2%e0%b9%80%e0%b8%aa%e0%b9%89%e0%b8%99%e0%b8%96%e0%b8%94%e0%b8%96\/","title":{"rendered":"\u0e27\u0e34\u0e18\u0e35\u0e2a\u0e23\u0e49\u0e32\u0e07 scatterplot \u0e14\u0e49\u0e27\u0e22\u0e40\u0e2a\u0e49\u0e19\u0e16\u0e14\u0e16\u0e2d\u0e22\u0e43\u0e19 r"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0e1a\u0e48\u0e2d\u0e22\u0e04\u0e23\u0e31\u0e49\u0e07\u0e40\u0e21\u0e37\u0e48\u0e2d\u0e40\u0e23\u0e32\u0e17\u0e33\u0e01\u0e32\u0e23\u0e16\u0e14\u0e16\u0e2d\u0e22\u0e40\u0e0a\u0e34\u0e07\u0e40\u0e2a\u0e49\u0e19\u0e2d\u0e22\u0e48\u0e32\u0e07\u0e07\u0e48\u0e32\u0e22 \u0e40\u0e23\u0e32\u0e15\u0e49\u0e2d\u0e07\u0e01\u0e32\u0e23\u0e2a\u0e23\u0e49\u0e32\u0e07\u0e41\u0e1c\u0e19\u0e20\u0e32\u0e1e\u0e01\u0e23\u0e30\u0e08\u0e32\u0e22\u0e40\u0e1e\u0e37\u0e48\u0e2d\u0e43\u0e2b\u0e49\u0e40\u0e2b\u0e47\u0e19\u0e20\u0e32\u0e1e\u0e01\u0e32\u0e23\u0e1c\u0e2a\u0e21\u0e04\u0e48\u0e32 x \u0e41\u0e25\u0e30 y \u0e41\u0e1a\u0e1a\u0e15\u0e48\u0e32\u0e07\u0e46<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0e42\u0e0a\u0e04\u0e14\u0e35\u0e17\u0e35\u0e48 R \u0e17\u0e33\u0e43\u0e2b\u0e49\u0e01\u0e32\u0e23\u0e2a\u0e23\u0e49\u0e32\u0e07\u0e1e\u0e2d\u0e22\u0e15\u0e4c\u0e04\u0e25\u0e32\u0e27\u0e14\u0e4c\u0e40\u0e1b\u0e47\u0e19\u0e40\u0e23\u0e37\u0e48\u0e2d\u0e07\u0e07\u0e48\u0e32\u0e22\u0e42\u0e14\u0e22\u0e43\u0e0a\u0e49\u0e1f\u0e31\u0e07\u0e01\u0e4c\u0e0a\u0e31\u0e19 <strong>plot()<\/strong> \u0e15\u0e31\u0e27\u0e2d\u0e22\u0e48\u0e32\u0e07\u0e40\u0e0a\u0e48\u0e19:<\/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=\"Scatterplot \u0e43\u0e19\u0e2d\u0e32\u0e23\u0e4c\" width=\"434\" height=\"396\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u0e19\u0e2d\u0e01\u0e08\u0e32\u0e01\u0e19\u0e35\u0e49\u0e22\u0e31\u0e07\u0e07\u0e48\u0e32\u0e22\u0e15\u0e48\u0e2d\u0e01\u0e32\u0e23\u0e40\u0e1e\u0e34\u0e48\u0e21\u0e40\u0e2a\u0e49\u0e19\u0e01\u0e32\u0e23\u0e16\u0e14\u0e16\u0e2d\u0e22\u0e25\u0e07\u0e43\u0e19 Scatterplot \u0e42\u0e14\u0e22\u0e43\u0e0a\u0e49\u0e1f\u0e31\u0e07\u0e01\u0e4c\u0e0a\u0e31\u0e19 <strong>abline()<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0e15\u0e31\u0e27\u0e2d\u0e22\u0e48\u0e32\u0e07\u0e40\u0e0a\u0e48\u0e19:<\/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=\"\u0e1e\u0e25\u0e47\u0e2d\u0e15\u0e01\u0e23\u0e30\u0e08\u0e32\u0e22\u0e1e\u0e23\u0e49\u0e2d\u0e21\u0e40\u0e2a\u0e49\u0e19\u0e16\u0e14\u0e16\u0e2d\u0e22\u0e43\u0e19 R\" width=\"438\" height=\"394\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u0e19\u0e2d\u0e01\u0e08\u0e32\u0e01\u0e19\u0e35\u0e49\u0e40\u0e23\u0e32\u0e22\u0e31\u0e07\u0e2a\u0e32\u0e21\u0e32\u0e23\u0e16\u0e40\u0e1e\u0e34\u0e48\u0e21\u0e40\u0e2a\u0e49\u0e19\u0e0a\u0e48\u0e27\u0e07\u0e04\u0e27\u0e32\u0e21\u0e21\u0e31\u0e48\u0e19\u0e43\u0e08\u0e43\u0e2b\u0e49\u0e01\u0e31\u0e1a\u0e1e\u0e25\u0e47\u0e2d\u0e15\u0e42\u0e14\u0e22\u0e43\u0e0a\u0e49\u0e1f\u0e31\u0e07\u0e01\u0e4c\u0e0a\u0e31\u0e19 <strong>\u0e17\u0e33\u0e19\u0e32\u0e22 () \u0e44\u0e14\u0e49<\/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=\"\u0e40\u0e2a\u0e49\u0e19\u0e01\u0e32\u0e23\u0e16\u0e14\u0e16\u0e2d\u0e22\u0e17\u0e35\u0e48\u0e21\u0e35\u0e0a\u0e48\u0e27\u0e07\u0e04\u0e27\u0e32\u0e21\u0e40\u0e0a\u0e37\u0e48\u0e2d\u0e21\u0e31\u0e48\u0e19\u0e43\u0e19 R\" width=\"430\" height=\"396\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u0e2b\u0e23\u0e37\u0e2d\u0e40\u0e23\u0e32\u0e2d\u0e32\u0e08\u0e40\u0e1e\u0e34\u0e48\u0e21\u0e1a\u0e23\u0e23\u0e17\u0e31\u0e14\u0e0a\u0e48\u0e27\u0e07\u0e40\u0e27\u0e25\u0e32\u0e01\u0e32\u0e23\u0e17\u0e33\u0e19\u0e32\u0e22\u0e25\u0e07\u0e43\u0e19\u0e1e\u0e25\u0e47\u0e2d\u0e15\u0e41\u0e17\u0e19\u0e42\u0e14\u0e22\u0e01\u0e32\u0e23\u0e23\u0e30\u0e1a\u0e38\u0e1b\u0e23\u0e30\u0e40\u0e20\u0e17\u0e0a\u0e48\u0e27\u0e07\u0e40\u0e27\u0e25\u0e32\u0e43\u0e19\u0e1f\u0e31\u0e07\u0e01\u0e4c\u0e0a\u0e31\u0e19 <strong>\u0e01\u0e32\u0e23\u0e17\u0e33\u0e19\u0e32\u0e22 ()<\/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=\"\u0e40\u0e2a\u0e49\u0e19\u0e01\u0e32\u0e23\u0e16\u0e14\u0e16\u0e2d\u0e22\u0e1e\u0e23\u0e49\u0e2d\u0e21\u0e40\u0e2a\u0e49\u0e19\u0e0a\u0e48\u0e27\u0e07\u0e40\u0e27\u0e25\u0e32\u0e01\u0e32\u0e23\u0e17\u0e33\u0e19\u0e32\u0e22\u0e43\u0e19 R\" width=\"432\" height=\"394\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u0e2a\u0e38\u0e14\u0e17\u0e49\u0e32\u0e22\u0e19\u0e35\u0e49 \u0e40\u0e23\u0e32\u0e2a\u0e32\u0e21\u0e32\u0e23\u0e16\u0e17\u0e33\u0e43\u0e2b\u0e49\u0e1e\u0e25\u0e47\u0e2d\u0e15\u0e21\u0e35\u0e04\u0e27\u0e32\u0e21\u0e2a\u0e27\u0e22\u0e07\u0e32\u0e21\u0e21\u0e32\u0e01\u0e02\u0e36\u0e49\u0e19\u0e44\u0e14\u0e49\u0e42\u0e14\u0e22\u0e01\u0e32\u0e23\u0e40\u0e1e\u0e34\u0e48\u0e21\u0e0a\u0e37\u0e48\u0e2d\u0e40\u0e23\u0e37\u0e48\u0e2d\u0e07 \u0e40\u0e1b\u0e25\u0e35\u0e48\u0e22\u0e19\u0e0a\u0e37\u0e48\u0e2d\u0e41\u0e01\u0e19 \u0e41\u0e25\u0e30\u0e40\u0e1b\u0e25\u0e35\u0e48\u0e22\u0e19\u0e23\u0e39\u0e1b\u0e23\u0e48\u0e32\u0e07\u0e02\u0e2d\u0e07\u0e08\u0e38\u0e14\u0e1e\u0e25\u0e47\u0e2d\u0e15\u0e41\u0e15\u0e48\u0e25\u0e30\u0e08\u0e38\u0e14<\/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=\"\u0e40\u0e2a\u0e49\u0e19\u0e01\u0e32\u0e23\u0e16\u0e14\u0e16\u0e2d\u0e22\u0e1e\u0e23\u0e49\u0e2d\u0e21 Scatterplot \u0e43\u0e19 R\" width=\"432\" height=\"417\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u0e41\u0e2b\u0e25\u0e48\u0e07\u0e02\u0e49\u0e2d\u0e21\u0e39\u0e25\u0e40\u0e1e\u0e34\u0e48\u0e21\u0e40\u0e15\u0e34\u0e21<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u0e1a\u0e17\u0e0a\u0e48\u0e27\u0e22\u0e2a\u0e2d\u0e19\u0e15\u0e48\u0e2d\u0e44\u0e1b\u0e19\u0e35\u0e49\u0e08\u0e30\u0e2d\u0e18\u0e34\u0e1a\u0e32\u0e22\u0e27\u0e34\u0e18\u0e35\u0e14\u0e33\u0e40\u0e19\u0e34\u0e19\u0e01\u0e32\u0e23\u0e07\u0e32\u0e19\u0e17\u0e31\u0e48\u0e27\u0e44\u0e1b\u0e2d\u0e37\u0e48\u0e19\u0e46 \u0e43\u0e19 R:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/th\/\u0e1b\u0e49\u0e32\u0e22\u0e1e\u0e2d\u0e22\u0e15\u0e4c\u0e04\u0e25\u0e32\u0e27\u0e14\u0e4c\u0e2d\u0e32\u0e23\u0e4c\/\" target=\"_blank\" rel=\"noopener\">\u0e27\u0e34\u0e18\u0e35\u0e15\u0e34\u0e14\u0e1b\u0e49\u0e32\u0e22\u0e01\u0e33\u0e01\u0e31\u0e1a\u0e08\u0e38\u0e14\u0e1a\u0e19 Scatterplot \u0e43\u0e19 R<\/a><br \/> <a href=\"https:\/\/statorials.org\/th\/\u0e1f\u0e31\u0e07\u0e01\u0e4c\u0e0a\u0e31\u0e19\u0e01\u0e23\u0e30\u0e27\u0e19\u0e01\u0e23\u0e30\u0e27\u0e32\u0e22\u0e43\u0e08-r\/\" target=\"_blank\" rel=\"noopener\">\u0e27\u0e34\u0e18\u0e35\u0e43\u0e0a\u0e49\u0e1f\u0e31\u0e07\u0e01\u0e4c\u0e0a\u0e31\u0e19 Jitter \u0e43\u0e19 R \u0e2a\u0e33\u0e2b\u0e23\u0e31\u0e1a point cloud<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0e1a\u0e48\u0e2d\u0e22\u0e04\u0e23\u0e31\u0e49\u0e07\u0e40\u0e21\u0e37\u0e48\u0e2d\u0e40\u0e23\u0e32\u0e17\u0e33\u0e01\u0e32\u0e23\u0e16\u0e14\u0e16\u0e2d\u0e22\u0e40\u0e0a\u0e34\u0e07\u0e40\u0e2a\u0e49\u0e19\u0e2d\u0e22\u0e48\u0e32\u0e07\u0e07\u0e48\u0e32\u0e22 \u0e40\u0e23\u0e32\u0e15\u0e49\u0e2d\u0e07\u0e01\u0e32\u0e23 [&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":[],"class_list":["post-683","post","type-post","status-publish","format-standard","hentry","category-3"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0e27\u0e34\u0e18\u0e35\u0e2a\u0e23\u0e49\u0e32\u0e07\u0e41\u0e1c\u0e19\u0e20\u0e39\u0e21\u0e34\u0e01\u0e23\u0e30\u0e08\u0e32\u0e22\u0e14\u0e49\u0e27\u0e22\u0e40\u0e2a\u0e49\u0e19\u0e01\u0e32\u0e23\u0e16\u0e14\u0e16\u0e2d\u0e22\u0e43\u0e19 R - Statology<\/title>\n<meta name=\"description\" content=\"\u0e04\u0e33\u0e2d\u0e18\u0e34\u0e1a\u0e32\u0e22\u0e07\u0e48\u0e32\u0e22\u0e46 \u0e40\u0e01\u0e35\u0e48\u0e22\u0e27\u0e01\u0e31\u0e1a\u0e27\u0e34\u0e18\u0e35\u0e2a\u0e23\u0e49\u0e32\u0e07 Scatterplot 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