{"id":1311,"date":"2023-07-26T22:17:32","date_gmt":"2023-07-26T22:17:32","guid":{"rendered":"https:\/\/statorials.org\/tr\/rde-standardize-edilmis-kalintilar\/"},"modified":"2023-07-26T22:17:32","modified_gmt":"2023-07-26T22:17:32","slug":"rde-standardize-edilmis-kalintilar","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/rde-standardize-edilmis-kalintilar\/","title":{"rendered":"R&#39;de standartla\u015ft\u0131r\u0131lm\u0131\u015f art\u0131klar nas\u0131l hesaplan\u0131r"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Art\u0131k,<\/strong> bir<a href=\"https:\/\/statorials.org\/tr\/dogrusal-regresyon-1\/\" target=\"_blank\" rel=\"noopener noreferrer\">regresyon modelinde<\/a> g\u00f6zlemlenen bir de\u011fer ile tahmin edilen bir de\u011fer aras\u0131ndaki farkt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Art\u0131k = G\u00f6zlemlenen de\u011fer \u2013 Tahmin edilen de\u011fer<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">G\u00f6zlemlenen de\u011ferleri \u00e7izer ve uygun regresyon \u00e7izgisini \u00fcst \u00fcste koyarsak, her <a href=\"https:\/\/statorials.org\/tr\/istatistikte-gozlem\/\" target=\"_blank\" rel=\"noopener\">g\u00f6zlem<\/a> i\u00e7in art\u0131klar, g\u00f6zlem ile regresyon \u00e7izgisi aras\u0131ndaki dikey mesafe olacakt\u0131r:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12422 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/residus1-1.png\" alt=\"\u0130statistiklerde art\u0131k \u00f6rne\u011fi\" width=\"487\" height=\"382\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bir regresyon modelinde ayk\u0131r\u0131 de\u011ferleri tan\u0131mlamak i\u00e7in s\u0131kl\u0131kla kulland\u0131\u011f\u0131m\u0131z bir t\u00fcr art\u0131k <strong>, standartla\u015ft\u0131r\u0131lm\u0131\u015f art\u0131k<\/strong> olarak adland\u0131r\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>r <sub>ben<\/sub> = e <sub>ben<\/sub> \/ s(e <sub>ben<\/sub> )<\/strong> = <strong>e <sub>ben<\/sub> \/ RSE\u221a <span style=\"border-top: 1px solid black;\">1-h <sub>ii<\/sub><\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>e <sub>i<\/sub> :<\/strong> i&#8217;inci <sup>kal\u0131nt\u0131<\/sup><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>RSE:<\/strong> modelin art\u0131k standart hatas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>h <sub>ii<\/sub><\/strong> : <sup>i&#8217;inci<\/sup> g\u00f6zlemin y\u00fckseli\u015fi<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Pratikte, mutlak de\u011feri 3&#8217;ten b\u00fcy\u00fck olan herhangi bir standartla\u015ft\u0131r\u0131lm\u0131\u015f art\u0131k de\u011feri genellikle ayk\u0131r\u0131 de\u011fer olarak kabul ederiz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu e\u011fitimde R&#8217;de standartla\u015ft\u0131r\u0131lm\u0131\u015f art\u0131klar\u0131n nas\u0131l hesaplanaca\u011f\u0131na dair ad\u0131m ad\u0131m bir \u00f6rnek sunulmaktad\u0131r.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>1. Ad\u0131m: Verileri girin<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u00d6ncelikle R&#8217;de \u00e7al\u0131\u015fmak i\u00e7in k\u00fc\u00e7\u00fck bir veri k\u00fcmesi olu\u015fturaca\u011f\u0131z:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create data<\/span>\ndata &lt;- data.frame(x=c(8, 12, 12, 13, 14, 16, 17, 22, 24, 26, 29, 30),\n                   y=c(41, 42, 39, 37, 35, 39, 45, 46, 39, 49, 55, 57))\n\n<span style=\"color: #008080;\">#viewdata\n<\/span>data\n\n    xy\n1 8 41\n2 12 42\n3 12 39\n4 13 37\n5 14 35\n6 16 39\n7 17 45\n8 22 46\n9 24 39\n10 26 49\n11 29 55\n12 30 57<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Ad\u0131m 2: Regresyon modelini yerle\u015ftirin<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Daha sonra <a href=\"https:\/\/statorials.org\/tr\/rde-basit-dogrusal-regresyon\/\" target=\"_blank\" rel=\"noopener\">basit bir do\u011frusal regresyon modeline<\/a> uyum sa\u011flamak i\u00e7in <strong>lm()<\/strong> fonksiyonunu kullanaca\u011f\u0131z:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#fit model\n<\/span>model &lt;- lm(y ~ x, data=data)\n\n<span style=\"color: #008080;\">#view model summary\n<span style=\"color: #000000;\">summary(model)<\/span> \n\n<span style=\"color: #000000;\">Call:\nlm(formula = y ~ x, data = data)\n\nResiduals:\n    Min 1Q Median 3Q Max \n-8.7578 -2.5161 0.0292 3.3457 5.3268 \n\nCoefficients:\n            Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) 29.6309 3.6189 8.188 9.6e-06 ***\nx 0.7553 0.1821 4.148 0.00199 ** \n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 4.442 on 10 degrees of freedom\nMultiple R-squared: 0.6324, Adjusted R-squared: 0.5956 \nF-statistic: 17.2 on 1 and 10 DF, p-value: 0.001988<\/span><\/span><\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Ad\u0131m 3: Standartla\u015ft\u0131r\u0131lm\u0131\u015f art\u0131klar\u0131 hesaplay\u0131n<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">Daha sonra, modelin standartla\u015ft\u0131r\u0131lm\u0131\u015f art\u0131klar\u0131n\u0131 hesaplamak i\u00e7in yerle\u015fik <strong>rstandard()<\/strong> fonksiyonunu kullanaca\u011f\u0131z:<\/span><\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#calculate the standardized residuals\n<\/span>standard_res &lt;- rstandard(model)\n\n<span style=\"color: #008080;\">#view the standardized residuals<\/span>\nstandard_res\n\n          1 2 3 4 5 6 \n 1.40517322 0.81017562 0.07491009 -0.59323342 -1.24820530 -0.64248883 \n          7 8 9 10 11 12 \n 0.59610905 -0.05876884 -2.11711982 -0.06655600 0.91057211 1.26973888\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u0130stersek standartla\u015ft\u0131r\u0131lm\u0131\u015f art\u0131klar\u0131 orijinal veri \u00e7er\u00e7evesine ekleyebiliriz:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#column bind standardized residuals back to original data frame\n<\/span>final_data &lt;- cbind(data, standard_res)\n\n<span style=\"color: #008080;\">#view data frame<\/span>\n    xy standard_res\n1 8 41 1.40517322\n2 12 42 0.81017562\n3 12 39 0.07491009\n4 13 37 -0.59323342\n5 14 35 -1.24820530\n6 16 39 -0.64248883\n7 17 45 0.59610905\n8 22 46 -0.05876884\n9 24 39 -2.11711982\n10 26 49 -0.06655600\n11 29 55 0.91057211\n12 30 57 1.26973888\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Daha sonra hangi g\u00f6zlemlerin ayk\u0131r\u0131 de\u011ferlere en yak\u0131n oldu\u011fu hakk\u0131nda bir fikir edinmek i\u00e7in her g\u00f6zlemi standartla\u015ft\u0131r\u0131lm\u0131\u015f kal\u0131nt\u0131s\u0131na g\u00f6re en b\u00fcy\u00fckten en k\u00fc\u00e7\u00fc\u011fe do\u011fru s\u0131ralayabiliriz:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#sort standardized residuals descending\n<span style=\"color: #000000;\">final_data[ <span style=\"color: #3366ff;\">order<\/span> (-standard_res),]\n\n    xy standard_res\n1 8 41 1.40517322\n12 30 57 1.26973888\n11 29 55 0.91057211\n2 12 42 0.81017562\n7 17 45 0.59610905\n3 12 39 0.07491009\n8 22 46 -0.05876884\n10 26 49 -0.06655600\n4 13 37 -0.59323342\n6 16 39 -0.64248883\n5 14 35 -1.24820530\n9 24 39 -2.11711982<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Sonu\u00e7lardan, standartla\u015ft\u0131r\u0131lm\u0131\u015f art\u0131klar\u0131n hi\u00e7birinin mutlak 3 de\u011ferini a\u015fmad\u0131\u011f\u0131n\u0131 g\u00f6rebiliriz. Dolay\u0131s\u0131yla g\u00f6zlemlerin hi\u00e7biri ayk\u0131r\u0131 g\u00f6r\u00fcnm\u00fcyor.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ad\u0131m 4: Standartla\u015ft\u0131r\u0131lm\u0131\u015f art\u0131klar\u0131 g\u00f6rselle\u015ftirin<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Son olarak, tahmin de\u011fi\u015fkeninin de\u011ferlerini standartla\u015ft\u0131r\u0131lm\u0131\u015f art\u0131klara g\u00f6re g\u00f6rselle\u015ftirmek i\u00e7in bir da\u011f\u0131l\u0131m grafi\u011fi olu\u015fturabiliriz:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008080;\">#plot predictor variable vs. standardized residuals\n<\/span>plot(final_data$x, standard_res, ylab=' <span style=\"color: #008000;\">Standardized Residuals<\/span> ', xlab=' <span style=\"color: #008000;\">x<\/span> ') \n\n<span style=\"color: #008080;\">#add horizontal line at 0\n<\/span>abline(0, 0)<\/span><\/span><\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/tr\/kalinti\/\" target=\"_blank\" rel=\"noopener\">Kal\u0131nt\u0131lar nelerdir?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/standartlastirilmis-kalintilar\/\">Standartla\u015ft\u0131r\u0131lm\u0131\u015f art\u0131klar nelerdir?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/coklu-dogrusal-regresyon\/\" target=\"_blank\" rel=\"noopener\">\u00c7oklu Do\u011frusal Regresyona Giri\u015f<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Art\u0131k, birregresyon modelinde g\u00f6zlemlenen bir de\u011fer ile tahmin edilen bir de\u011fer aras\u0131ndaki farkt\u0131r. A\u015fa\u011f\u0131daki \u015fekilde hesaplan\u0131r: Art\u0131k = G\u00f6zlemlenen de\u011fer \u2013 Tahmin edilen de\u011fer G\u00f6zlemlenen de\u011ferleri \u00e7izer ve uygun regresyon \u00e7izgisini \u00fcst \u00fcste koyarsak, her g\u00f6zlem i\u00e7in art\u0131klar, g\u00f6zlem ile regresyon \u00e7izgisi aras\u0131ndaki dikey mesafe olacakt\u0131r: Bir regresyon modelinde ayk\u0131r\u0131 de\u011ferleri tan\u0131mlamak i\u00e7in s\u0131kl\u0131kla kulland\u0131\u011f\u0131m\u0131z [&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-1311","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>R&#039;de 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