{"id":317,"date":"2023-08-02T14:35:00","date_gmt":"2023-08-02T14:35:00","guid":{"rendered":"https:\/\/statorials.org\/tr\/degisen-varyans\/"},"modified":"2023-08-02T14:35:00","modified_gmt":"2023-08-02T14:35:00","slug":"degisen-varyans","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/degisen-varyans\/","title":{"rendered":"Heteroskedastisite"},"content":{"rendered":"<p>Bu makale istatistikte de\u011fi\u015fen varyans\u0131n ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. Ek olarak de\u011fi\u015fen varyansa neyin sebep oldu\u011funu, sonu\u00e7lar\u0131n\u0131n neler oldu\u011funu ve nas\u0131l d\u00fczeltilece\u011fini \u00f6\u011freneceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-heterocedasticidad\"><\/span> Heteroskedastisite nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0130statistiklerde <strong>heteroskedastisite<\/strong> , hata varyans\u0131n\u0131n sabit olmad\u0131\u011f\u0131n\u0131 ima eden bir regresyon modeli sunan bir \u00f6zelliktir. Ba\u015fka bir deyi\u015fle, heteroskedastik bir model, hatalar\u0131n\u0131n d\u00fczensiz varyansa sahip oldu\u011fu anlam\u0131na gelir, bu durumda modele heteroskedastik denir.<\/p>\n<p> Hatan\u0131n (veya kal\u0131nt\u0131n\u0131n), ger\u00e7ek de\u011fer ile regresyon modeli taraf\u0131ndan tahmin edilen de\u011fer aras\u0131ndaki fark olarak tan\u0131mland\u0131\u011f\u0131n\u0131 unutmay\u0131n.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-2028e64ca2c0035860e93c4bf244e2f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e_i=y_i-\\widehat{y}_i\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"87\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Regresyon modeli olu\u015fturulurken her g\u00f6zlemin yapt\u0131\u011f\u0131 hata \u00f6nceki ifade kullan\u0131larak hesaplan\u0131r. Bu nedenle, hesaplanan hatalar\u0131n <a href=\"https:\/\/statorials.org\/tr\/varyans\/\">varyans\u0131n\u0131n<\/a> g\u00f6zlemler boyunca sabit olmad\u0131\u011f\u0131, aksine de\u011fi\u015fti\u011fi zaman istatistiksel bir model de\u011fi\u015fen varyansl\u0131d\u0131r. <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/homoscedasticite-et-heteroscedasticite.png\" alt=\"heteroskedastisite ve homoskedastisite\" class=\"wp-image-6840\" width=\"581\" height=\"226\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Her ne kadar \u00e7ok basit g\u00f6r\u00fcnse de regresyon modelinin heteroskedastisite g\u00f6stermemesi \u00f6nemlidir, \u00e7\u00fcnk\u00fc modelin hesaplanmas\u0131 art\u0131klar\u0131n varyans\u0131n\u0131n sabit oldu\u011fu ger\u00e7e\u011fine dayanmaktad\u0131r, asl\u0131nda regresyon modelinin \u00f6nceki varsay\u0131mlar\u0131ndan biridir. regresyon modelleri.<\/p>\n<p> White testi veya Goldfeld-Quandt testi gibi heteroskedastisiteyi tespit edebilen belirli istatistiksel testler vard\u0131r. Ancak genellikle art\u0131klar\u0131n grafi\u011fini \u00e7izerek bunlar\u0131n de\u011fi\u015fen varyanslar\u0131 belirlenebilir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"causas-de-la-heterocedasticidad\"><\/span> Heteroskedastisitenin nedenleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bir modelde de\u011fi\u015fen varyans\u0131n en yayg\u0131n nedenleri \u015funlard\u0131r:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Veri aral\u0131\u011f\u0131 ortalamaya g\u00f6re \u00e7ok geni\u015f oldu\u011funda. Ayn\u0131 istatistiksel \u00f6rnekte \u00e7ok b\u00fcy\u00fck de\u011ferler ve \u00e7ok k\u00fc\u00e7\u00fck de\u011ferler varsa elde edilen regresyon modelinin de\u011fi\u015fen varyansl\u0131 olmas\u0131 muhtemeldir.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Regresyon modelinde de\u011fi\u015fkenlerin g\u00f6z ard\u0131 edilmesi ayn\u0131 zamanda de\u011fi\u015fen varyansla da sonu\u00e7lan\u0131r. Mant\u0131ksal olarak, e\u011fer ilgili bir de\u011fi\u015fken modele dahil edilmemi\u015fse, bu de\u011fi\u015fkenin de\u011fi\u015fimi art\u0131klara dahil edilecek ve bunun mutlaka sabitlenmesi gerekmeyecektir.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Benzer \u015fekilde yap\u0131daki bir de\u011fi\u015fiklik, modelin veri setine zay\u0131f bir \u015fekilde uyum sa\u011flamas\u0131na neden olabilir ve dolay\u0131s\u0131yla art\u0131klar\u0131n varyans\u0131 sabit olmayabilir.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Baz\u0131 de\u011fi\u015fkenler di\u011fer a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenlerden \u00e7ok daha b\u00fcy\u00fck de\u011ferlere sahip oldu\u011funda model de\u011fi\u015fen varyansa sahip olabilir. Bu durumda problemin \u00e7\u00f6z\u00fcm\u00fc i\u00e7in de\u011fi\u015fkenler g\u00f6receli hale getirilebilir.<\/span><\/li>\n<\/ul>\n<p> Ancak baz\u0131 durumlar\u0131n do\u011fas\u0131 gere\u011fi de\u011fi\u015fen varyans sergilemesi muhtemeldir. \u00d6rne\u011fin, bir ki\u015finin gelirini g\u0131da harcamalar\u0131na g\u00f6re modellersek, zengin insanlar\u0131n g\u0131da harcamalar\u0131nda fakir insanlara g\u00f6re \u00e7ok daha fazla de\u011fi\u015fkenlik oldu\u011funu g\u00f6r\u00fcr\u00fcz. \u00c7\u00fcnk\u00fc zengin bir ki\u015fi, her zaman ucuz restoranlarda yemek yiyen fakir bir insan\u0131n aksine, bazen pahal\u0131 restoranlarda, bazen de ucuz restoranlarda yemek yer. Bu nedenle regresyon modelinin heteroskedastisiteye sahip olmas\u0131 kolayd\u0131r. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"consecuencias-de-la-heterocedasticidad\"><\/span> De\u011fi\u015fen varyans\u0131n sonu\u00e7lar\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Temel olarak bir regresyon modelinde heteroskedastisitenin sonu\u00e7lar\u0131 a\u015fa\u011f\u0131daki gibidir:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Hatalar\u0131n karelerinin ortalamas\u0131 olarak tan\u0131mlanan en k\u00fc\u00e7\u00fck kareler tahmincisinde verimlilik kaybolur.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">En k\u00fc\u00e7\u00fck kareler tahmincilerinin <a href=\"https:\/\/statorials.org\/tr\/kovaryans-matrisi\/\">kovaryans matrisinin<\/a> hesaplanmas\u0131nda hatalar meydana gelmektedir.<\/span> <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"corregir-la-heterocedasticidad\"><\/span> Do\u011fru de\u011fi\u015fen varyans<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ortaya \u00e7\u0131kan regresyon modeli de\u011fi\u015fen varyansl\u0131 oldu\u011funda, de\u011fi\u015fen varyans elde etmek i\u00e7in a\u015fa\u011f\u0131daki d\u00fczeltmeleri deneyebiliriz:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Ba\u011f\u0131ms\u0131z de\u011fi\u015fkenin do\u011fal logaritmas\u0131n\u0131 hesaplay\u0131n; bu genellikle grafikte art\u0131klar\u0131n varyans\u0131 artt\u0131\u011f\u0131nda kullan\u0131\u015fl\u0131d\u0131r.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Art\u0131k grafi\u011fine ba\u011fl\u0131 olarak, ba\u011f\u0131ms\u0131z de\u011fi\u015fkenin ba\u015fka bir d\u00f6n\u00fc\u015f\u00fcm t\u00fcr\u00fc daha pratik olabilir. \u00d6rne\u011fin grafik parabol \u015feklinde ise ba\u011f\u0131ms\u0131z de\u011fi\u015fkenin karesini hesaplay\u0131p o de\u011fi\u015fkeni modele ekleyebiliriz.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Model i\u00e7in ba\u015fka de\u011fi\u015fkenler de kullan\u0131labilir; Bir de\u011fi\u015fkeni \u00e7\u0131kararak veya ekleyerek art\u0131klar\u0131n varyans\u0131 de\u011fi\u015ftirilebilir.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">En k\u00fc\u00e7\u00fck kareler kriteri yerine a\u011f\u0131rl\u0131kl\u0131 en k\u00fc\u00e7\u00fck kareler kriteri kullan\u0131labilir.<\/span> <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"heterocedasticidad-y-homocedasticidad\"><\/span> De\u011fi\u015fken varyans ve e\u015f varyans<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Son olarak istatistikte de\u011fi\u015fen varyans ile e\u015f varyans aras\u0131ndaki farklar\u0131n neler oldu\u011funu g\u00f6rece\u011fiz, \u00e7\u00fcnk\u00fc bunlar regresyon modellerinin a\u00e7\u0131k bir \u015fekilde belirtmemiz gereken iki kavram\u0131d\u0131r.<\/p>\n<p> Bir regresyon modelinin <strong>e\u015fvaryansl\u0131l\u0131\u011f\u0131,<\/strong> hata varyans\u0131n\u0131n sabit oldu\u011funu g\u00f6steren istatistiksel bir \u00f6zelliktir. Dolay\u0131s\u0131yla, homoskedastik bir model, hatalar\u0131n\u0131n varyans\u0131n\u0131n sabit oldu\u011fu anlam\u0131na gelir.<\/p>\n<p> <strong>Heteroskedastisite ve homoskedastisite aras\u0131ndaki fark,<\/strong> art\u0131klar\u0131n varyans\u0131n\u0131n sabitli\u011finde bulunur. Bir modelin art\u0131klar\u0131n\u0131n varyans\u0131 sabit de\u011filse bu, modelin de\u011fi\u015fen varyansl\u0131 oldu\u011fu anlam\u0131na gelir. \u00d6te yandan, art\u0131klar\u0131n varyans\u0131 sabitse bu, onun homoskedastik oldu\u011fu anlam\u0131na gelir.<\/p>\n<p> Dolay\u0131s\u0131yla kurdu\u011fumuz regresyon modelinin homoskedastik olmas\u0131n\u0131 sa\u011flamam\u0131z gerekiyor, b\u00f6ylece art\u0131klar\u0131n varyans\u0131n\u0131n sabit oldu\u011fu varsay\u0131m\u0131 kar\u015f\u0131lanm\u0131\u015f olacakt\u0131r. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/es-varyanslilik\/\">Homoskedasticity<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makale istatistikte de\u011fi\u015fen varyans\u0131n ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. Ek olarak de\u011fi\u015fen varyansa neyin sebep oldu\u011funu, sonu\u00e7lar\u0131n\u0131n neler oldu\u011funu ve nas\u0131l d\u00fczeltilece\u011fini \u00f6\u011freneceksiniz. Heteroskedastisite nedir? \u0130statistiklerde heteroskedastisite , hata varyans\u0131n\u0131n sabit olmad\u0131\u011f\u0131n\u0131 ima eden bir regresyon modeli sunan bir \u00f6zelliktir. Ba\u015fka bir deyi\u015fle, heteroskedastik bir model, hatalar\u0131n\u0131n d\u00fczensiz varyansa sahip oldu\u011fu anlam\u0131na gelir, bu durumda modele [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"class_list":["post-317","post","type-post","status-publish","format-standard","hentry","category-istatistik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 De\u011fi\u015fken varyans<\/title>\n<meta name=\"description\" content=\"Burada istatistikte de\u011fi\u015fen varyans\u0131n ne oldu\u011funu, nedenlerini, sonu\u00e7lar\u0131n\u0131 ve bir modelin de\u011fi\u015fen varyans\u0131n\u0131n nas\u0131l d\u00fczeltilece\u011fini ke\u015ffedeceksiniz.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, 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