{"id":1153,"date":"2023-07-27T11:55:28","date_gmt":"2023-07-27T11:55:28","guid":{"rendered":"https:\/\/statorials.org\/tr\/coklu-dogrusal-regresyon\/"},"modified":"2023-07-27T11:55:28","modified_gmt":"2023-07-27T11:55:28","slug":"coklu-dogrusal-regresyon","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/coklu-dogrusal-regresyon\/","title":{"rendered":"\u00c7oklu do\u011frusal regresyona giri\u015f"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Tek bir yorday\u0131c\u0131 de\u011fi\u015fken ile bir yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkiyi anlamak istedi\u011fimizde genellikle<a href=\"https:\/\/statorials.org\/tr\/dogrusal-regresyon-1\/\" target=\"_blank\" rel=\"noopener noreferrer\">basit do\u011frusal regresyon<\/a> kullan\u0131r\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak <em>birden fazla<\/em> yorday\u0131c\u0131 de\u011fi\u015fken ile bir yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkiyi anlamak istiyorsak <strong>\u00e7oklu do\u011frusal regresyon<\/strong> kullanabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">E\u011fer <em>p<\/em> tane \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkenimiz varsa, \u00e7oklu do\u011frusal regresyon modeli \u015fu formu al\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Y = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub> X <sub>1<\/sub> <sub>+<\/sub> \u03b2 <sub>2<\/sub> X <sub>2<\/sub> + \u2026 + \u03b2 <sub>p<\/sub><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Y<\/strong> : Yan\u0131t de\u011fi\u015fkeni<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>X <sub>j<\/sub><\/strong> : <sup>j&#8217;inci<\/sup> tahmin de\u011fi\u015fkeni<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>\u03b2j<\/sub><\/strong> : Di\u011fer t\u00fcm belirleyicileri sabit tutarak, <sub>Xj&#8217;deki<\/sub> bir birimlik art\u0131\u015f\u0131n Y \u00fczerindeki ortalama etkisi<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03b5<\/strong> : Hata terimi<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u03b2 <sub>0<\/sub> , \u03b2 <sub>1<\/sub> , B <sub>2<\/sub> , \u2026, \u03b2 <sub>p<\/sub> de\u011ferleri, art\u0131klar\u0131n karelerinin toplam\u0131n\u0131 (RSS) en aza indiren <strong>en k\u00fc\u00e7\u00fck kareler y\u00f6ntemi<\/strong> kullan\u0131larak se\u00e7ilir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>RSS = \u03a3(y <sub>ben<\/sub> \u2013 \u0177 <sub>ben<\/sub> ) <sup>2<\/sup><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> : <em>Toplam<\/em> anlam\u0131na gelen bir Yunan sembol\u00fc<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>y <sub>i<\/sub><\/strong> : <sup>i&#8217;inci<\/sup> g\u00f6zlem i\u00e7in ger\u00e7ek yan\u0131t de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u0177 <sub>i<\/sub><\/strong> : \u00c7oklu do\u011frusal regresyon modeline dayal\u0131 olarak tahmin edilen yan\u0131t de\u011feri<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu katsay\u0131 tahminlerini bulmak i\u00e7in kullan\u0131lan y\u00f6ntem matris cebirine ba\u011fl\u0131d\u0131r ve burada ayr\u0131nt\u0131lara girmeyece\u011fiz. Neyse ki herhangi bir istatistik yaz\u0131l\u0131m\u0131 bu katsay\u0131lar\u0131 sizin i\u00e7in hesaplayabilir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00c7oklu do\u011frusal regresyon \u00e7\u0131kt\u0131s\u0131 nas\u0131l yorumlan\u0131r<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Tahmin edici de\u011fi\u015fkenleri <em>, \u00e7al\u0131\u015f\u0131lan saatleri<\/em> ve <em>girilen haz\u0131rl\u0131k s\u0131navlar\u0131n\u0131n<\/em> yan\u0131 s\u0131ra cevap de\u011fi\u015fkeni <em>s\u0131nav puan\u0131n\u0131<\/em> kullanarak \u00e7oklu do\u011frusal regresyon modeli uydurdu\u011fumuzu varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki ekran g\u00f6r\u00fcnt\u00fcs\u00fc bu model i\u00e7in \u00e7oklu do\u011frusal regresyon sonucunun nas\u0131l g\u00f6r\u00fcnebilece\u011fini g\u00f6stermektedir:<\/span><\/p>\n<p> <em><span style=\"color: #000000;\"><strong>Not:<\/strong> A\u015fa\u011f\u0131daki ekran g\u00f6r\u00fcnt\u00fcs\u00fc <a href=\"https:\/\/statorials.org\/tr\/coklu-dogrusal-regresyon-excel\/\" target=\"_blank\" rel=\"noopener noreferrer\">Excel i\u00e7in \u00e7oklu do\u011frusal regresyon \u00e7\u0131kt\u0131s\u0131n\u0131<\/a> g\u00f6sterir, ancak \u00e7\u0131kt\u0131da g\u00f6sterilen say\u0131lar herhangi bir istatistiksel yaz\u0131l\u0131m\u0131 kullanarak g\u00f6rece\u011finiz regresyon \u00e7\u0131kt\u0131s\u0131n\u0131n tipik bir \u00f6rne\u011fidir.<\/span><\/em> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-6301 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/multipleregexcel4.png\" alt=\"\u00c7oklu Do\u011frusal Regresyon Sonu\u00e7lar\u0131n\u0131 Yorumlama\" width=\"557\" height=\"385\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Model sonu\u00e7lar\u0131ndan elde edilen katsay\u0131lar, tahmini bir \u00e7oklu do\u011frusal regresyon modeli olu\u015fturmam\u0131za olanak tan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>S\u0131nav puan\u0131 = 67,67 + 5,56*(saat) \u2013 0,60*(haz\u0131rl\u0131k s\u0131navlar\u0131)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Katsay\u0131lar\u0131 yorumlaman\u0131n yolu a\u015fa\u011f\u0131daki gibidir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><em>Deneme s\u0131navlar\u0131n\u0131n sabit kald\u0131\u011f\u0131 varsay\u0131ld\u0131\u011f\u0131nda,<\/em> \u00e7al\u0131\u015fma saatindeki her bir birimlik ilave art\u0131\u015f, s\u0131nav puan\u0131nda ortalama <strong>5,56<\/strong> puanl\u0131k bir art\u0131\u015fla ili\u015fkilidir.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Haz\u0131rl\u0131k s\u0131navlar\u0131ndaki her bir birimlik art\u0131\u015f <em>, \u00e7al\u0131\u015f\u0131lan saat say\u0131s\u0131n\u0131n sabit kald\u0131\u011f\u0131 varsay\u0131ld\u0131\u011f\u0131nda<\/em> , s\u0131nav puan\u0131nda ortalama <strong>0,60<\/strong> puanl\u0131k bir d\u00fc\u015f\u00fc\u015fe yol a\u00e7maktad\u0131r.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu modeli ayn\u0131 zamanda \u00f6\u011frencinin toplam ders saati ve girdi\u011fi haz\u0131rl\u0131k s\u0131navlar\u0131na g\u00f6re alaca\u011f\u0131 beklenen s\u0131nav notunu belirlemek i\u00e7in de kullanabiliriz. \u00d6rne\u011fin 4 saat ders \u00e7al\u0131\u015f\u0131p 1 haz\u0131rl\u0131k s\u0131nav\u0131na giren bir \u00f6\u011frencinin s\u0131nav puan\u0131n\u0131n <strong>89,31<\/strong> olmas\u0131 gerekir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">S\u0131nav puan\u0131 = 67,67 + 5,56*(4) -0,60*(1) = <strong>89,31<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Model sonu\u00e7lar\u0131n\u0131n geri kalan\u0131n\u0131 \u015fu \u015fekilde yorumlayabilirsiniz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>R-Kare:<\/strong> Buna belirleme katsay\u0131s\u0131 denir. A\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenler taraf\u0131ndan a\u00e7\u0131klanabilen yan\u0131t de\u011fi\u015fkeninin varyans\u0131n\u0131n oran\u0131d\u0131r. Bu \u00f6rnekte s\u0131nav puanlar\u0131ndaki farkl\u0131l\u0131\u011f\u0131n %73,4&#8217;\u00fc \u00e7al\u0131\u015f\u0131lan saat ve girilen haz\u0131rl\u0131k s\u0131nav\u0131 say\u0131s\u0131yla a\u00e7\u0131klanmaktad\u0131r.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Standart hata:<\/strong> G\u00f6zlemlenen de\u011ferler ile regresyon \u00e7izgisi aras\u0131ndaki ortalama mesafedir. Bu \u00f6rnekte g\u00f6zlemlenen de\u011ferler regresyon do\u011frusundan ortalama 5.366 birim sapmaktad\u0131r.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>F:<\/strong> Bu, Regresyon MS\/Kalan MS olarak hesaplanan, regresyon modelinin genel F istatisti\u011fidir.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>F Anlam\u0131:<\/strong> Bu, genel F istatisti\u011fiyle ili\u015fkili p de\u011feridir. Bu bize regresyon modelinin bir b\u00fct\u00fcn olarak istatistiksel olarak anlaml\u0131 olup olmad\u0131\u011f\u0131n\u0131 s\u00f6yler. Ba\u015fka bir deyi\u015fle, bize iki a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenin birle\u015fiminin yan\u0131t de\u011fi\u015fkeni ile istatistiksel olarak anlaml\u0131 bir ili\u015fkiye sahip olup olmad\u0131\u011f\u0131n\u0131 s\u00f6yler. Bu durumda p de\u011feri 0,05&#8217;ten k\u00fc\u00e7\u00fckt\u00fcr; bu durum a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenlerin, \u00e7al\u0131\u015f\u0131lan saatlerin ve girilen haz\u0131rl\u0131k s\u0131navlar\u0131n\u0131n birle\u015fiminin s\u0131nav sonucuyla istatistiksel olarak anlaml\u0131 bir ili\u015fkiye sahip oldu\u011funu g\u00f6sterir.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Katsay\u0131n\u0131n P de\u011ferleri.<\/strong> Bireysel p de\u011ferleri bize her a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenin istatistiksel olarak anlaml\u0131 olup olmad\u0131\u011f\u0131n\u0131 s\u00f6yler. \u00c7al\u0131\u015f\u0131lan saatlerin istatistiksel olarak anlaml\u0131 oldu\u011funu (p = 0,00), al\u0131nan haz\u0131rl\u0131k s\u0131navlar\u0131n\u0131n (p = 0,52) \u03b1 = 0,05&#8217;te istatistiksel olarak anlaml\u0131 olmad\u0131\u011f\u0131n\u0131 g\u00f6rebiliriz. Ge\u00e7mi\u015f haz\u0131rl\u0131k s\u0131navlar\u0131n\u0131n istatistiksel olarak anlaml\u0131 olmamas\u0131 nedeniyle onlar\u0131 modelden \u00e7\u0131karmaya karar verebiliriz.<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>\u00c7oklu do\u011frusal regresyon modelinin uyumu nas\u0131l de\u011ferlendirilir?<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u00c7oklu do\u011frusal regresyon modelinin bir veri k\u00fcmesine ne kadar iyi &#8220;uydu\u011funu&#8221; de\u011ferlendirmek i\u00e7in yayg\u0131n olarak iki say\u0131 kullan\u0131l\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> <strong>R-kare:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/degiskenleri-aciklayici-yanitlar\/\" target=\"_blank\" rel=\"noopener noreferrer\">Yan\u0131t de\u011fi\u015fkenindeki<\/a> varyans\u0131n yorday\u0131c\u0131 de\u011fi\u015fkenler taraf\u0131ndan a\u00e7\u0131klanabilen oran\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">R-kare de\u011feri 0 ila 1 aras\u0131nda de\u011fi\u015febilir. 0 de\u011feri, yan\u0131t de\u011fi\u015fkeninin yorday\u0131c\u0131 de\u011fi\u015fken taraf\u0131ndan hi\u00e7bir \u015fekilde a\u00e7\u0131klanamayaca\u011f\u0131n\u0131 g\u00f6sterir. 1 de\u011feri, yan\u0131t de\u011fi\u015fkeninin yorday\u0131c\u0131 de\u011fi\u015fken taraf\u0131ndan hatas\u0131z olarak m\u00fckemmel bir \u015fekilde a\u00e7\u0131klanabilece\u011fini g\u00f6sterir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir modelin R karesi ne kadar y\u00fcksek olursa, model verilere o kadar iyi uyum sa\u011flayabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Standart hata:<\/strong> G\u00f6zlemlenen de\u011ferler ile regresyon \u00e7izgisi aras\u0131ndaki ortalama mesafedir. Standart hata ne kadar k\u00fc\u00e7\u00fck olursa, model verilere o kadar iyi uyum sa\u011flayabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir regresyon modeli kullanarak tahminlerde bulunmak istiyorsak, regresyonun standart hatas\u0131 R-kareden daha yararl\u0131 bir \u00f6l\u00e7\u00fcm olabilir \u00e7\u00fcnk\u00fc bize tahminlerimizin birim cinsinden ne kadar do\u011fru oldu\u011funa dair bir fikir verir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Model uyumunu de\u011ferlendirmek i\u00e7in R-kare ve standart hatan\u0131n kullan\u0131lmas\u0131n\u0131n art\u0131lar\u0131 ve eksileri hakk\u0131nda tam bir a\u00e7\u0131klama i\u00e7in a\u015fa\u011f\u0131daki makalelere bak\u0131n:<\/span><\/p>\n<ul>\n<li> <a href=\"https:\/\/statorials.org\/tr\/iyi-r-kare-degeri\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u0130yi bir R-kare de\u011feri nedir?<\/a><\/li>\n<li> <a href=\"https:\/\/statorials.org\/tr\/standart-hata-regresyonu\/\" target=\"_blank\" rel=\"noopener noreferrer\">Regresyon modelinin standart hatas\u0131n\u0131 anlama<\/a><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>\u00c7oklu Do\u011frusal Regresyon Varsay\u0131mlar\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u00c7oklu do\u011frusal regresyon, verilerle ilgili d\u00f6rt temel varsay\u0131mda bulunur:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Do\u011frusal ili\u015fki:<\/strong> Ba\u011f\u0131ms\u0131z de\u011fi\u015fken x ile ba\u011f\u0131ml\u0131 de\u011fi\u015fken y aras\u0131nda do\u011frusal bir ili\u015fki vard\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Ba\u011f\u0131ms\u0131zl\u0131k:<\/strong> Art\u0131klar ba\u011f\u0131ms\u0131zd\u0131r. \u00d6zellikle zaman serisi verilerinde ard\u0131\u015f\u0131k art\u0131klar aras\u0131nda bir korelasyon yoktur.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. Homoskedastisite:<\/strong> Art\u0131klar x&#8217;in her seviyesinde sabit bir varyansa sahiptir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>4. Normallik:<\/strong> Model art\u0131klar\u0131 normal da\u011f\u0131l\u0131ma sahiptir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu hipotezlerin nas\u0131l test edilece\u011fine ili\u015fkin tam bir a\u00e7\u0131klama i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/dogrusal-regresyon-varsayimlari\/\" target=\"_blank\" rel=\"noopener noreferrer\">bu makaleye<\/a> bak\u0131n.<\/span><\/p>\n<h3> <strong>Yaz\u0131l\u0131m kullanarak \u00e7oklu do\u011frusal regresyon<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimlerde, farkl\u0131 istatistiksel yaz\u0131l\u0131mlar kullan\u0131larak \u00e7oklu do\u011frusal regresyonun nas\u0131l ger\u00e7ekle\u015ftirilece\u011fine ili\u015fkin ad\u0131m ad\u0131m \u00f6rnekler verilmektedir:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/coklu-dogrusal-regresyon-r\/\" target=\"_blank\" rel=\"noopener noreferrer\">R&#8217;de \u00e7oklu do\u011frusal regresyon nas\u0131l ger\u00e7ekle\u015ftirilir<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/dogrusal-regresyon-pitonu\/\" target=\"_blank\" rel=\"noopener noreferrer\">Python&#8217;da \u00e7oklu do\u011frusal regresyon nas\u0131l ger\u00e7ekle\u015ftirilir<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/coklu-dogrusal-regresyon-excel\/\" target=\"_blank\" rel=\"noopener noreferrer\">Excel&#8217;de \u00e7oklu do\u011frusal regresyon nas\u0131l ger\u00e7ekle\u015ftirilir<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/spss-coklu-dogrusal-regresyon\/\" target=\"_blank\" rel=\"noopener noreferrer\">SPSS&#8217;de \u00e7oklu do\u011frusal regresyon nas\u0131l ger\u00e7ekle\u015ftirilir<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/coklu-dogrusal-regresyon-istatistikleri\/\" target=\"_blank\" rel=\"noopener noreferrer\">Stata&#8217;da \u00e7oklu do\u011frusal regresyon nas\u0131l ger\u00e7ekle\u015ftirilir<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/dogrusal-regresyon-google-sayfalari\/\" target=\"_blank\" rel=\"noopener noreferrer\">Google E-Tablolarda do\u011frusal regresyon nas\u0131l ger\u00e7ekle\u015ftirilir?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tek bir yorday\u0131c\u0131 de\u011fi\u015fken ile bir yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkiyi anlamak istedi\u011fimizde genelliklebasit do\u011frusal regresyon kullan\u0131r\u0131z. Ancak birden fazla yorday\u0131c\u0131 de\u011fi\u015fken ile bir yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkiyi anlamak istiyorsak \u00e7oklu do\u011frusal regresyon kullanabiliriz. E\u011fer p tane \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkenimiz varsa, \u00e7oklu do\u011frusal regresyon modeli \u015fu formu al\u0131r: Y = \u03b2 0 + \u03b2 1 X 1 [&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-1153","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>\u00c7oklu Do\u011frusal Regresyona Giri\u015f - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitim, makine \u00f6\u011freniminde en s\u0131k kullan\u0131lan tekniklerden biri olan \u00e7oklu do\u011frusal regresyona h\u0131zl\u0131 bir giri\u015f sa\u011flar.\" \/>\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\/coklu-dogrusal-regresyon\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u00c7oklu Do\u011frusal Regresyona Giri\u015f - 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