{"id":508,"date":"2023-07-29T16:29:54","date_gmt":"2023-07-29T16:29:54","guid":{"rendered":"https:\/\/statorials.org\/tr\/asci-mesafesini-kullanarak-etkili-veri-noktalarinin-nasil-belirlenecegi\/"},"modified":"2023-07-29T16:29:54","modified_gmt":"2023-07-29T16:29:54","slug":"asci-mesafesini-kullanarak-etkili-veri-noktalarinin-nasil-belirlenecegi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/asci-mesafesini-kullanarak-etkili-veri-noktalarinin-nasil-belirlenecegi\/","title":{"rendered":"Cook mesafesini kullanarak etkili veri noktalar\u0131 nas\u0131l belirlenir?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u00c7o\u011funlukla D <sub>i<\/sub> olarak g\u00f6sterilen <strong>Cook mesafesi<\/strong> , regresyon modelinizi olumsuz y\u00f6nde etkileyebilecek etkili veri noktalar\u0131n\u0131 tan\u0131mlamak i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/coklu-dogrusal-regresyon\/\" target=\"_blank\" rel=\"noopener noreferrer\">regresyon analizinde<\/a> kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Cook mesafesinin form\u00fcl\u00fc:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>d <sub>ben<\/sub><\/strong> = (r <sub>i<\/sub> <sup>2<\/sup> \/ p*MSE) * (h <sub>ii<\/sub> \/ (1-h <sub>ii<\/sub> ) <sup>2<\/sup> )<\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>r<\/strong> <sub><strong>i<\/strong><\/sub> <sup>i&#8217;inci<\/sup> kal\u0131nt\u0131d\u0131r<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p<\/strong> , regresyon modelindeki katsay\u0131lar\u0131n say\u0131s\u0131d\u0131r<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>MSE<\/strong> ortalama kare hatas\u0131d\u0131r<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>h<\/strong> <sub>ii<\/sub> <sup>i&#8217;inci<\/sup> kald\u0131ra\u00e7 de\u011feridir<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Form\u00fcl biraz karma\u015f\u0131k g\u00f6r\u00fcnse de iyi haber \u015fu ki \u00e7o\u011fu istatistik yaz\u0131l\u0131m\u0131 bunu sizin i\u00e7in kolayca hesaplayabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Cook&#8217;un mesafesi esasen tek bir \u015fey yapar: <strong><sup>i&#8217;inci<\/sup> veri noktas\u0131 kald\u0131r\u0131ld\u0131\u011f\u0131nda modelin t\u00fcm uydurulmu\u015f de\u011ferlerinin ne kadar de\u011fi\u015fti\u011fini \u00f6l\u00e7er.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Cook mesafesi i\u00e7in y\u00fcksek bir de\u011fere sahip bir veri noktas\u0131, bunun uygun de\u011ferleri g\u00fc\u00e7l\u00fc bir \u015fekilde etkiledi\u011fini g\u00f6sterir. Genel bir kural, Cook mesafesi 4\/n&#8217;den b\u00fcy\u00fck olan herhangi bir noktan\u0131n ( <em>burada n, toplam veri noktas\u0131 say\u0131s\u0131d\u0131r<\/em> ) ayk\u0131r\u0131 de\u011fer olarak kabul edilmesidir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Cook mesafesinin genellikle etkili veri noktalar\u0131n\u0131 <em>tan\u0131mlamak<\/em> i\u00e7in kullan\u0131ld\u0131\u011f\u0131n\u0131 unutmamak \u00f6nemlidir. Bir veri noktas\u0131n\u0131n etkili olmas\u0131 onun mutlaka kald\u0131r\u0131lmas\u0131 gerekti\u011fi anlam\u0131na gelmez. \u00d6ncelikle veri noktas\u0131n\u0131n yanl\u0131\u015f kaydedilip kaydedilmedi\u011fini veya veri noktas\u0131nda ilgin\u00e7 bir bulguya i\u015faret edebilecek tuhaf bir \u015fey olup olmad\u0131\u011f\u0131n\u0131 kontrol etmelisiniz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>R&#8217;de Cook&#8217;un mesafesi nas\u0131l hesaplan\u0131r<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnek Cook&#8217;un mesafesinin R cinsinden nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6stermektedir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6ncelikle bu \u00f6rnek i\u00e7in ihtiya\u00e7 duyaca\u011f\u0131m\u0131z iki k\u00fct\u00fcphaneyi y\u00fckleyece\u011fiz:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong>library(ggplot2)\nlibrary(gridExtra)<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Daha sonra iki veri \u00e7er\u00e7evesi tan\u0131mlayaca\u011f\u0131z: biri iki ayk\u0131r\u0131 de\u011fer i\u00e7eren ve di\u011feri ayk\u0131r\u0131 olmayan.<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create data frame with no outliers<\/span>\nno_outliers &lt;- data.frame(x = c(1, 2, 2, 3, 4, 5, 7, 3, 2, 12, 11, 15, 14, 17, 22),\n                          y = c(22, 23, 24, 23, 19, 34, 35, 36, 36, 34, 32, 38, 41,\n                                42, 44))\n\n<span style=\"color: #008080;\">#create data frame with two outliers\n<\/span>outliers &lt;- data.frame(x = c(1, 2, 2, 3, 4, 5, 7, 3, 2, 12, 11, 15, 14, 17, 22),\n                       y = c( <span style=\"color: #800080;\">190<\/span> , 23, 24, 23, 19, 34, 35, 36, 36, 34, 32, 38, 41,\n                             42, <span style=\"color: #800080;\">180<\/span> ))<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Daha sonra, iki veri \u00e7er\u00e7evesini yan yana g\u00f6r\u00fcnt\u00fclemek i\u00e7in bir da\u011f\u0131l\u0131m grafi\u011fi olu\u015fturaca\u011f\u0131z:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create scatterplot for data frame with no outliers\n<\/span>no_outliers_plot &lt;- ggplot(data = no_outliers, aes(x = x, y = y)) +\n  geom_point() +\n  geom_smooth(method = lm) +\n  ylim(0, 200) +\n  ggtitle(\"No Outliers\")\n\n<span style=\"color: #008080;\">#create scatterplot for data frame with outliers\n<\/span>outliers_plot &lt;- ggplot(data = outliers, aes(x = x, y = y)) +\n  geom_point() +\n  geom_smooth(method = lm) +\n  ylim(0, 200) +\n  ggtitle(\"With Outliers\")\n\n<span style=\"color: #008080;\">#plot the two scatterplots side by side\n<\/span>gridExtra::grid.arrange(no_outliers_plot, outliers_plot, ncol=2)<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Ayk\u0131r\u0131 de\u011ferlerin regresyon \u00e7izgisinin uyumunu nas\u0131l olumsuz etkiledi\u011fini ikinci grafikte g\u00f6rebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130kinci veri k\u00fcmesindeki etkili noktalar\u0131 belirlemek i\u00e7in, veri k\u00fcmesindeki her g\u00f6zlem i\u00e7in <strong>Cook mesafesini<\/strong> hesaplayabilir ve ard\u0131ndan hangi g\u00f6zlemlerin geleneksel 4\/n e\u015fi\u011finin \u00fczerinde oldu\u011funu g\u00f6rmek i\u00e7in bu mesafeleri \u00e7izebiliriz:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#fit the linear regression model to the dataset with outliers<\/span>\nmodel &lt;- lm(y ~ x, data = outliers)\n\n<span style=\"color: #008080;\">#find Cook's distance for each observation in the dataset\n<\/span>cooksD &lt;- cooks.distance(model)\n\n<span style=\"color: #008080;\"># Plot Cook's Distance with a horizontal line at 4\/n to see which observations<\/span>\n<span style=\"color: #008080;\">#exceed this threshold<\/span>\nn &lt;- nrow(outliers)\nplot(cooksD, main = \"Cooks Distance for Influential Obs\")\nabline(h = 4\/n, lty = 2, col = \"steelblue\") <span style=\"color: #008080;\"># add cutoff line<\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Veri setindeki ilk ve son g\u00f6zlemin 4\/n e\u015fi\u011fini a\u015ft\u0131\u011f\u0131n\u0131 a\u00e7\u0131k\u00e7a g\u00f6rebiliyoruz. Dolay\u0131s\u0131yla bu iki g\u00f6zlemi, regresyon modelini olumsuz y\u00f6nde etkileyen etkili veri noktalar\u0131 olarak tan\u0131mlayaca\u011f\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">4\/n e\u015fi\u011fini a\u015fan t\u00fcm g\u00f6zlemleri kald\u0131rmak istiyorsak bunu a\u015fa\u011f\u0131daki kodu kullanarak yapabiliriz:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#identify influential points<\/span>\ninfluential_obs &lt;- as.numeric(names(cooksD)[(cooksD &gt; (4\/n))])\n\n<span style=\"color: #008080;\">#define new data frame with influential points removed\n<\/span>outliers_removed &lt;- outliers[-influential_obs, ]<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Daha sonra iki da\u011f\u0131l\u0131m grafi\u011fini kar\u015f\u0131la\u015ft\u0131rabiliriz: biri mevcut etki noktalar\u0131yla birlikte regresyon \u00e7izgisini g\u00f6sterir, di\u011feri ise etki noktalar\u0131 kald\u0131r\u0131lm\u0131\u015f olarak regresyon \u00e7izgisini g\u00f6sterir:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create scatterplot with outliers present<\/span>\noutliers_present &lt;- ggplot(data = outliers, aes(x = x, y = y)) +\n  geom_point() +\n  geom_smooth(method = lm) +\n  ylim(0, 200) +\n  ggtitle(\"Outliers Present\")\n\n<span style=\"color: #008080;\">#create scatterplot with outliers removed<\/span>\noutliers_removed &lt;- ggplot(data = outliers_removed, aes(x = x, y = y)) +\n  geom_point() +\n  geom_smooth(method = lm) +\n  ylim(0, 200) +\n  ggtitle(\"Outliers Removed\")\n\n<span style=\"color: #008080;\">#plot both scatterplots side by side\n<\/span>gridExtra::grid.arrange(outliers_present, outliers_removed, ncol = 2)<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u0130ki etkili veri noktas\u0131 kald\u0131r\u0131ld\u0131\u011f\u0131nda regresyon \u00e7izgisinin verilere ne kadar iyi uydu\u011funu a\u00e7\u0131k\u00e7a g\u00f6rebiliriz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Teknik notlar<\/strong><\/span><\/h3>\n<ul>\n<li> <span style=\"color: #000000;\">\u00c7o\u011fu istatistiksel yaz\u0131l\u0131m, bir veri setindeki her g\u00f6zlem i\u00e7in Cook&#8217;un mesafesini kolayca hesaplama yetene\u011fine sahiptir.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Cook&#8217;s Distance&#8217;\u0131n yaln\u0131zca etki noktalar\u0131n\u0131 <em>belirlemenin<\/em> bir yolu oldu\u011funu unutmay\u0131n.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Etkili noktalarla <em>ba\u015fa \u00e7\u0131kman\u0131n<\/em> bir\u00e7ok yolu vard\u0131r; bunlar aras\u0131nda bu noktalar\u0131 kald\u0131rmak, bu noktalar\u0131 ortalama veya medyan gibi bir de\u011ferle de\u011fi\u015ftirmek veya noktalar\u0131 modelde tutmak ancak sonu\u00e7lar\u0131n gerilemesini bildirirken bunlar\u0131 dikkatli bir \u015fekilde not etmek yer al\u0131r.<\/span><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u00c7o\u011funlukla D i olarak g\u00f6sterilen Cook mesafesi , regresyon modelinizi olumsuz y\u00f6nde etkileyebilecek etkili veri noktalar\u0131n\u0131 tan\u0131mlamak i\u00e7in regresyon analizinde kullan\u0131l\u0131r. Cook mesafesinin form\u00fcl\u00fc: d ben = (r i 2 \/ p*MSE) * (h ii \/ (1-h ii ) 2 ) Alt\u0131n: r i i&#8217;inci kal\u0131nt\u0131d\u0131r p , regresyon modelindeki katsay\u0131lar\u0131n say\u0131s\u0131d\u0131r MSE ortalama kare [&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-508","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>Cook Mesafesini Kullanarak Etkili Veri Noktalar\u0131 Nas\u0131l Belirlenir - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde Cook mesafesini kullanarak regresyon analizinde etkili veri noktalar\u0131n\u0131n nas\u0131l belirlenece\u011fi a\u00e7\u0131klanmaktad\u0131r.\" \/>\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\/tr\/asci-mesafesini-kullanarak-etkili-veri-noktalarinin-nasil-belirlenecegi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Cook Mesafesini Kullanarak Etkili Veri Noktalar\u0131 Nas\u0131l Belirlenir - 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