{"id":1333,"date":"2023-07-26T20:26:36","date_gmt":"2023-07-26T20:26:36","guid":{"rendered":"https:\/\/statorials.org\/tr\/pagan-breusch-testi\/"},"modified":"2023-07-26T20:26:36","modified_gmt":"2023-07-26T20:26:36","slug":"pagan-breusch-testi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/pagan-breusch-testi\/","title":{"rendered":"Breusch-pagan testi: tan\u0131m ve \u00f6rnek"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/dogrusal-regresyon-varsayimlari\/\" target=\"_blank\" rel=\"noopener\">Do\u011frusal regresyonun temel varsay\u0131mlar\u0131ndan<\/a> biri, <a href=\"https:\/\/statorials.org\/tr\/kalinti\/\" target=\"_blank\" rel=\"noopener\">art\u0131klar\u0131n<\/a> , yorday\u0131c\u0131 de\u011fi\u015fkenin her d\u00fczeyinde e\u015fit varyansla da\u011f\u0131ld\u0131\u011f\u0131d\u0131r. Bu varsay\u0131ma <strong>e\u015f varyansl\u0131l\u0131k<\/strong> denir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu varsay\u0131ma uyulmad\u0131\u011f\u0131 takdirde art\u0131klarda <a href=\"https:\/\/statorials.org\/tr\/degisen-varyans-regresyonu\/\" target=\"_blank\" rel=\"noopener\">de\u011fi\u015fen varyans\u0131n<\/a> mevcut oldu\u011fu s\u00f6ylenir. Bu durumda regresyon sonu\u00e7lar\u0131 g\u00fcvenilmez hale gelir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">De\u011fi\u015fen varyans\u0131n mevcut olup olmad\u0131\u011f\u0131n\u0131 g\u00f6rsel olarak tespit etmenin bir yolu, regresyon modelinden uygun de\u011ferlere kar\u015f\u0131 art\u0131klar\u0131n bir grafi\u011fini olu\u015fturmakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Art\u0131klar grafikte daha y\u00fcksek de\u011ferlerde daha fazla yay\u0131l\u0131rsa, bu de\u011fi\u015fen varyans\u0131n varl\u0131\u011f\u0131n\u0131n bir g\u00f6stergesidir.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-13011 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/het2.jpg\" alt=\"Breusch-Pagan testi i\u00e7in de\u011fi\u015fen varyans \u00f6rne\u011fi\" width=\"484\" height=\"367\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">De\u011fi\u015fen varyans\u0131n mevcut olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullanabilece\u011fimiz resmi bir istatistiksel test <strong>Breusch-Pagan testidir<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu e\u011fitimde Breusch-Pagan testinin k\u0131sa bir a\u00e7\u0131klamas\u0131 ve bir \u00f6rnek verilmektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Breusch-Pagan testi nedir?<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>Breusch-Pagan testi,<\/strong> bir regresyon modelinde heteroskedastisitenin mevcut olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Test a\u015fa\u011f\u0131daki bo\u015f ve alternatif <a href=\"https:\/\/statorials.org\/tr\/hipotez-testi-1\/\" target=\"_blank\" rel=\"noopener\">hipotezleri<\/a> kullan\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Bo\u015f hipotez (H <sub>0<\/sub> ): E\u015f<\/strong> varyans mevcut (art\u0131klar e\u015fit varyansla da\u011f\u0131t\u0131l\u0131yor)<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Alternatif hipotez ( <sub>HA<\/sub> ):<\/strong> de\u011fi\u015fen varyans mevcut (art\u0131klar e\u015fit varyansla da\u011f\u0131lm\u0131yor)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Testin p de\u011feri belirli bir <a href=\"https:\/\/statorials.org\/tr\/p-degerleri-istatistiksel-anlamlilik\/\" target=\"_blank\" rel=\"noopener\">anlaml\u0131l\u0131k d\u00fczeyinin<\/a> alt\u0131ndaysa (yani, \u03b1 = 0,05), o zaman bo\u015f hipotezi reddederiz ve regresyon modelinde de\u011fi\u015fen varyans\u0131n mevcut oldu\u011fu sonucuna var\u0131r\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Breusch-Pagan testini ger\u00e7ekle\u015ftirmek i\u00e7in a\u015fa\u011f\u0131daki ad\u0131mlar\u0131 kullan\u0131yoruz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> Regresyon modelini yerle\u015ftirin.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2.<\/strong> Model art\u0131klar\u0131n\u0131n karelerini hesaplay\u0131n.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3.<\/strong> Art\u0131klar\u0131n karelerini yan\u0131t de\u011ferleri olarak kullanarak yeni bir regresyon modeli uydurun.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>4.<\/strong> Ki-kare X <sup>2<\/sup> test istatisti\u011fini n*R <sup>2<\/sup> <sub>new<\/sub> formunda hesaplay\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> Toplam <a href=\"https:\/\/statorials.org\/tr\/istatistikte-gozlem\/\" target=\"_blank\" rel=\"noopener\">g\u00f6zlem<\/a> say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>R <sup>2<\/sup> <sub>yeni<\/sub> :<\/strong> Art\u0131klar\u0131n karelerini yan\u0131t de\u011ferleri olarak kullanan yeni regresyon modelinin R karesi<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">P (tahmin edicilerin say\u0131s\u0131) serbestlik derecesine sahip bu ki-kare testi istatisti\u011fine kar\u015f\u0131l\u0131k gelen <em>p<\/em> de\u011feri belirli bir anlaml\u0131l\u0131k d\u00fczeyinin alt\u0131ndaysa (yani \u03b1 = 0,05), o zaman bo\u015f hipotezi reddedin ve heteroskedastisitenin mevcut oldu\u011fu sonucuna var\u0131n .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Aksi halde s\u0131f\u0131r hipotezini reddetmeyin. Bu durumda homoskedastisitenin mevcut oldu\u011fu varsay\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00c7o\u011fu istatistik yaz\u0131l\u0131m\u0131n\u0131n Breusch-Pagan testini kolayca ger\u00e7ekle\u015ftirebildi\u011fini, dolay\u0131s\u0131yla bu ad\u0131mlar\u0131 muhtemelen hi\u00e7bir zaman elle uygulaman\u0131z gerekmeyece\u011fini unutmay\u0131n, ancak perde arkas\u0131nda neler olup bitti\u011fini bilmek yararl\u0131 olacakt\u0131r.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Breusch-Pagan testinin bir \u00f6rne\u011fi<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">10 farkl\u0131 basketbol oyuncusu hakk\u0131nda bilgi i\u00e7eren a\u015fa\u011f\u0131daki veri setine sahip oldu\u011fumuzu varsayal\u0131m:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-13013 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/pb1-1.png\" alt=\"\" width=\"283\" height=\"301\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u0130statistiksel yaz\u0131l\u0131m kullanarak a\u015fa\u011f\u0131daki <a href=\"https:\/\/statorials.org\/tr\/coklu-dogrusal-regresyon\/\" target=\"_blank\" rel=\"noopener\">\u00e7oklu do\u011frusal regresyon modelini<\/a> uyguluyoruz:<\/span><\/p>\n<p> <span style=\"color: #000000;\">skor = 62,47 + 1,12*(say\u0131) + 0,88*(asist) \u2013 0,43*(ribaund)<\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra bu modeli her oyuncunun reytingi hakk\u0131nda tahminler yapmak ve karesel art\u0131klar\u0131 (yani tahmin edilen reyting ile ger\u00e7ek reyting aras\u0131ndaki kare fark\u0131n\u0131) hesaplamak i\u00e7in kullan\u0131r\u0131z:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-13015 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/pb2-1.png\" alt=\"\" width=\"491\" height=\"296\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra, art\u0131klar\u0131n karelerini yan\u0131t de\u011ferleri olarak ve orijinal \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkenleri de yorday\u0131c\u0131 de\u011fi\u015fkenler olarak kullanarak yeni bir regresyon modeli uyguluyoruz. A\u015fa\u011f\u0131dakileri bulduk:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>say\u0131:<\/strong> 10<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sup>R2<\/sup> <sub>yeni<\/sub> :<\/strong> 0,600395<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Dolay\u0131s\u0131yla Breusch-Pagan testi i\u00e7in Ki-kare testi istatisti\u011fimiz n*R <sup>2<\/sup> <sub>yeni<\/sub> = 10*.600395 = <strong>6,00395&#8217;tir<\/strong> . Serbestlik dereceleri <em>p<\/em> = 3 \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkendir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/ki-kare-p-degeri-hesaplayici\/\" target=\"_blank\" rel=\"noopener\">Ki kare-P de\u011feri hesaplay\u0131c\u0131s\u0131na<\/a> g\u00f6re, 3 serbestlik dereceli <sup>X2<\/sup> = 6,00395&#8217;e kar\u015f\u0131l\u0131k gelen p de\u011feri <strong>0,111418&#8217;dir<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu p de\u011feri 0,05&#8217;ten k\u00fc\u00e7\u00fck olmad\u0131\u011f\u0131ndan s\u0131f\u0131r hipotezini reddedemiyoruz. Bu nedenle e\u015f varyansl\u0131l\u0131\u011f\u0131n mevcut oldu\u011funu varsay\u0131yoruz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Breusch-Pagan testi pratikte<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimlerde Breusch-Pagan testinin farkl\u0131 istatistiksel programlarda nas\u0131l ger\u00e7ekle\u015ftirilece\u011fine ili\u015fkin ad\u0131m ad\u0131m \u00f6rnekler verilmektedir:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/breusch-pagan-excel-testi\/\" target=\"_blank\" rel=\"noopener\">Excel&#8217;de Breusch-Pagan Testi Nas\u0131l Ger\u00e7ekle\u015ftirilir<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/breusch-pagan-testi-r\/\" target=\"_blank\" rel=\"noopener\">R&#8217;de Breusch-Pagan testi nas\u0131l yap\u0131l\u0131r<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/breusch-pagan-testi-pitonu\/\" target=\"_blank\" rel=\"noopener\">Python&#8217;da Breusch-Pagan testi nas\u0131l yap\u0131l\u0131r<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/breusch-pagan-stata-testi\/\" target=\"_blank\" rel=\"noopener\">Stata&#8217;da Breusch-Pagan testi nas\u0131l yap\u0131l\u0131r?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Do\u011frusal regresyonun temel varsay\u0131mlar\u0131ndan biri, art\u0131klar\u0131n , yorday\u0131c\u0131 de\u011fi\u015fkenin her d\u00fczeyinde e\u015fit varyansla da\u011f\u0131ld\u0131\u011f\u0131d\u0131r. Bu varsay\u0131ma e\u015f varyansl\u0131l\u0131k denir. Bu varsay\u0131ma uyulmad\u0131\u011f\u0131 takdirde art\u0131klarda de\u011fi\u015fen varyans\u0131n mevcut oldu\u011fu s\u00f6ylenir. Bu durumda regresyon sonu\u00e7lar\u0131 g\u00fcvenilmez hale gelir. De\u011fi\u015fen varyans\u0131n mevcut olup olmad\u0131\u011f\u0131n\u0131 g\u00f6rsel olarak tespit etmenin bir yolu, regresyon modelinden uygun de\u011ferlere kar\u015f\u0131 art\u0131klar\u0131n bir grafi\u011fini [&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-1333","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>Breusch-Pagan testi: tan\u0131m ve \u00f6rnek - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde resmi bir tan\u0131m ve bir \u00f6rnek de dahil olmak \u00fczere Breusch-Pagan testine basit bir giri\u015f sa\u011flanmaktad\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\/pagan-breusch-testi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Breusch-Pagan testi: tan\u0131m ve \u00f6rnek - 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