{"id":1624,"date":"2023-07-25T15:02:33","date_gmt":"2023-07-25T15:02:33","guid":{"rendered":"https:\/\/statorials.org\/tr\/artik-varyans\/"},"modified":"2023-07-25T15:02:33","modified_gmt":"2023-07-25T15:02:33","slug":"artik-varyans","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/artik-varyans\/","title":{"rendered":"Kalan bo\u015fluk nedir? (tan\u0131m &amp; #038; \u00f6rnek)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Art\u0131k varyans<\/strong> (bazen &#8220;a\u00e7\u0131klanamayan varyans&#8221; olarak da adland\u0131r\u0131l\u0131r), bir modeldeki model de\u011fi\u015fkenleri taraf\u0131ndan a\u00e7\u0131klanamayan varyans\u0131 ifade eder.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir modelin art\u0131k varyans\u0131 ne kadar y\u00fcksek olursa, model verilerdeki de\u011fi\u015fimi o kadar az a\u00e7\u0131klayabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130ki farkl\u0131 istatistiksel modelin sonu\u00e7lar\u0131nda art\u0131k varyans ortaya \u00e7\u0131k\u0131yor:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. ANOVA:<\/strong> \u00fc\u00e7 veya daha fazla ba\u011f\u0131ms\u0131z grubun ortalamalar\u0131n\u0131 kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Regresyon:<\/strong> Bir veya daha fazla \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fken ile bir <a href=\"https:\/\/statorials.org\/tr\/degiskenleri-aciklayici-yanitlar\/\" target=\"_blank\" rel=\"noopener\">yan\u0131t de\u011fi\u015fkeni<\/a> aras\u0131ndaki ili\u015fkiyi \u00f6l\u00e7mek i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler, bu y\u00f6ntemlerin her birindeki art\u0131k varyans\u0131n nas\u0131l yorumlanaca\u011f\u0131n\u0131 g\u00f6stermektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>ANOVA modellerinde kalan varyans<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir ANOVA (\u201cvaryans analizi\u201d) modelini her yerle\u015ftirdi\u011fimizde, a\u015fa\u011f\u0131dakine benzeyen bir ANOVA tablosu elde ederiz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-16075 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/varresiduelle1.png\" alt=\"ANOVA modelinde kalan varyans\" width=\"511\" height=\"140\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">ANOVA modelinden kalan varyans de\u011feri <strong>, grup i\u00e7i<\/strong> varyasyon i\u00e7in SS (&#8220;kareler toplam\u0131&#8221;) s\u00fctununda bulunur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu de\u011fer ayn\u0131 zamanda &#8220;hatalar\u0131n karelerinin toplam\u0131&#8221; olarak da adland\u0131r\u0131l\u0131r ve a\u015fa\u011f\u0131daki form\u00fcl kullan\u0131larak hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03a3(X <sub>ij<\/sub> \u2013 <span style=\"text-decoration: overline;\">X<\/span> <sub>j<\/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>\u03a3<\/strong> : \u201ctoplam\u201d anlam\u0131na gelen Yunanca bir sembol<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>X <sub>ij<\/sub><\/strong> : j grubunun <sup>i&#8217;inci<\/sup> g\u00f6zlemi<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">X<\/span> <sub>j<\/sub><\/strong> : j grubunun ortalamas\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Yukar\u0131daki ANOVA modelinde art\u0131k varyans\u0131n 1100,6 oldu\u011funu g\u00f6r\u00fcyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu art\u0131k varyans\u0131n &#8220;y\u00fcksek&#8221; olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in, gruplar i\u00e7indeki ortalama kareler toplam\u0131n\u0131 ve gruplar aras\u0131ndaki ortalama kareler toplam\u0131n\u0131 hesaplayabilir ve ikisi aras\u0131ndaki oran\u0131 bulabiliriz; bu, ANOVA tablosundaki genel F de\u011ferini verir.<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">F = MS <sub>girer<\/sub> \/ MS <sub>girer<\/sub><\/span><\/li>\n<li> <span style=\"color: #000000;\">F = 96,1 \/ 40,76296<\/span><\/li>\n<li> <span style=\"color: #000000;\">F = 2,357<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Yukar\u0131daki ANOVA tablosunda F de\u011feri 2,357 ve buna kar\u015f\u0131l\u0131k gelen p de\u011feri 0,113848&#8217;dir. Bu p de\u011feri \u03b1 = 0,05&#8217;ten k\u00fc\u00e7\u00fck olmad\u0131\u011f\u0131ndan s\u0131f\u0131r hipotezini reddetmek i\u00e7in yeterli kan\u0131t\u0131m\u0131z yok.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu, kar\u015f\u0131la\u015ft\u0131rd\u0131\u011f\u0131m\u0131z gruplar aras\u0131ndaki ortalama fark\u0131n \u00f6nemli \u00f6l\u00e7\u00fcde farkl\u0131 oldu\u011funu s\u00f6ylemek i\u00e7in yeterli kan\u0131ta sahip olmad\u0131\u011f\u0131m\u0131z anlam\u0131na geliyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu bize ANOVA modelinin art\u0131k varyans\u0131n\u0131n, modelin ger\u00e7ekte a\u00e7\u0131klayabildi\u011fi varyasyonla kar\u015f\u0131la\u015ft\u0131r\u0131ld\u0131\u011f\u0131nda y\u00fcksek oldu\u011funu s\u00f6yler.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Regresyon modellerinde kalan varyans<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir regresyon modelinde art\u0131k varyans, tahmin edilen veri noktalar\u0131 ile g\u00f6zlemlenen veri noktalar\u0131 aras\u0131ndaki farklar\u0131n karelerinin toplam\u0131 olarak tan\u0131mlan\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03a3(\u0177 <sub>ben<\/sub> \u2013 y <sub>ben<\/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>\u03a3<\/strong> : \u201ctoplam\u201d anlam\u0131na gelen Yunanca bir sembol<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u0177 <sub>i<\/sub> :<\/strong> Tahmin edilen veri noktalar\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>y <sub>i<\/sub> :<\/strong> G\u00f6zlemlenen veri noktalar\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bir regresyon modelini uydurdu\u011fumuzda genellikle a\u015fa\u011f\u0131dakine benzer bir sonu\u00e7 elde ederiz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-16077\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/varresiduel2-1.png\" alt=\"Regresyon modelinde kalan varyans\" width=\"488\" height=\"404\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">ANOVA modelinden elde edilen art\u0131k varyans de\u011feri, art\u0131k varyasyon i\u00e7in SS (\u201ckareler toplam\u0131\u201d) s\u00fctununda bulunabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Modeldeki art\u0131k varyasyonun toplam varyasyona oran\u0131 bize, yan\u0131t de\u011fi\u015fkenindeki, modeldeki yorday\u0131c\u0131 de\u011fi\u015fkenler taraf\u0131ndan a\u00e7\u0131klanamayan varyasyonun y\u00fczdesini anlat\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin yukar\u0131daki tabloda bu y\u00fczdeyi \u015fu \u015fekilde hesaplayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">A\u00e7\u0131klanamayan de\u011fi\u015fim = SS Art\u0131k \/ SS Toplam\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\">A\u00e7\u0131klanamayan varyasyon = 5,9024 \/ 174,5<\/span><\/li>\n<li> <span style=\"color: #000000;\">A\u00e7\u0131klanamayan varyasyon = 0,0338<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu de\u011fer a\u015fa\u011f\u0131daki form\u00fcl kullan\u0131larak da hesaplanabilir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">A\u00e7\u0131klanamayan varyasyon = 1 \u2013 R <sup>2<\/sup><\/span><\/li>\n<li> <span style=\"color: #000000;\">A\u00e7\u0131klanamayan varyasyon = 1 \u2013 0,96617<\/span><\/li>\n<li> <span style=\"color: #000000;\">A\u00e7\u0131klanamayan varyasyon = 0,0338<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Modelin R-kare de\u011feri bize, yorday\u0131c\u0131 de\u011fi\u015fken taraf\u0131ndan a\u00e7\u0131klanabilecek yan\u0131t de\u011fi\u015fkenindeki varyasyonun y\u00fczdesini verir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Dolay\u0131s\u0131yla, a\u00e7\u0131klanamayan varyasyon ne kadar d\u00fc\u015f\u00fck olursa, bir model, yan\u0131t de\u011fi\u015fkenindeki varyasyonu a\u00e7\u0131klamak i\u00e7in yorday\u0131c\u0131 de\u011fi\u015fkenleri kullanma konusunda o kadar yetenekli olur.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/tr\/iyi-r-kare-degeri\/\" target=\"_blank\" rel=\"noopener\">\u0130yi bir R-kare de\u011feri nedir?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/r-kare-excel\/\" target=\"_blank\" rel=\"noopener\">Excel&#8217;de R-kare nas\u0131l hesaplan\u0131r<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/r-uzeri-rnin-karesi\/\" target=\"_blank\" rel=\"noopener\">R&#8217;de R-kare nas\u0131l hesaplan\u0131r<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Art\u0131k varyans (bazen &#8220;a\u00e7\u0131klanamayan varyans&#8221; olarak da adland\u0131r\u0131l\u0131r), bir modeldeki model de\u011fi\u015fkenleri taraf\u0131ndan a\u00e7\u0131klanamayan varyans\u0131 ifade eder. Bir modelin art\u0131k varyans\u0131 ne kadar y\u00fcksek olursa, model verilerdeki de\u011fi\u015fimi o kadar az a\u00e7\u0131klayabilir. \u0130ki farkl\u0131 istatistiksel modelin sonu\u00e7lar\u0131nda art\u0131k varyans ortaya \u00e7\u0131k\u0131yor: 1. ANOVA: \u00fc\u00e7 veya daha fazla ba\u011f\u0131ms\u0131z grubun ortalamalar\u0131n\u0131 kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in kullan\u0131l\u0131r. 2. Regresyon: [&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-1624","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>Kalan bo\u015fluk nedir? 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Daha fazlas\u0131n\u0131 bil","sameAs":["https:\/\/statorials.org\/tr"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/posts\/1624","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/comments?post=1624"}],"version-history":[{"count":0,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/posts\/1624\/revisions"}],"wp:attachment":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/media?parent=1624"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/categories?post=1624"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/tags?post=1624"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}