{"id":2561,"date":"2023-07-21T17:48:35","date_gmt":"2023-07-21T17:48:35","guid":{"rendered":"https:\/\/statorials.org\/tr\/sasta-basit-dogrusal-regresyon\/"},"modified":"2023-07-21T17:48:35","modified_gmt":"2023-07-21T17:48:35","slug":"sasta-basit-dogrusal-regresyon","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/sasta-basit-dogrusal-regresyon\/","title":{"rendered":"Sas&#39;ta basit do\u011frusal regresyon nas\u0131l ger\u00e7ekle\u015ftirilir?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/dogrusal-regresyon-1\/\" target=\"_blank\" rel=\"noopener noreferrer\">Basit do\u011frusal regresyon,<\/a> yorday\u0131c\u0131 de\u011fi\u015fken ile <a href=\"https:\/\/statorials.org\/tr\/degiskenleri-aciklayici-yanitlar\/\" target=\"_blank\" rel=\"noopener noreferrer\">yan\u0131t de\u011fi\u015fkeni<\/a> aras\u0131ndaki ili\u015fkiyi anlamak i\u00e7in kullanabilece\u011fimiz bir tekniktir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu teknik, verilere en iyi &#8220;uyan&#8221; \u00e7izgiyi bulur ve a\u015fa\u011f\u0131daki formu al\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u0177 = b <sub>0<\/sub> + b <sub>1<\/sub> x<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u0177<\/strong> : Tahmini yan\u0131t de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>b <sub>0<\/sub><\/strong> : Regresyon \u00e7izgisinin ba\u015flang\u0131c\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>b <sub>1<\/sub><\/strong> : Regresyon \u00e7izgisinin e\u011fimi<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu denklem, yorday\u0131c\u0131 de\u011fi\u015fken ile yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkiyi anlamam\u0131za yard\u0131mc\u0131 olur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki ad\u0131m ad\u0131m \u00f6rnek, SAS&#8217;ta basit bir do\u011frusal regresyonun nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini g\u00f6sterir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><b>1. Ad\u0131m: Verileri olu\u015fturun<\/b><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte 15 \u00f6\u011frencinin toplam ders saatini ve final s\u0131nav notunu i\u00e7eren bir veri seti olu\u015fturaca\u011f\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tahmin edici de\u011fi\u015fken olarak <em>saatleri<\/em> ve yan\u0131t de\u011fi\u015fkeni olarak <em>puan\u0131<\/em> kullanarak basit bir do\u011frusal regresyon modeli uygulayaca\u011f\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, bu veri k\u00fcmesinin SAS&#8217;ta nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">\/*create dataset*\/\n<\/span><span style=\"color: #800080;\">data<\/span> exam_data;\n    <span style=\"color: #3366ff;\">input<\/span> hours score;\n    <span style=\"color: #3366ff;\">datalines<\/span> ;\n1 64\n2 66\n4 76\n5 73\n5 74\n6 81\n6 83\n7 82\n8 80\n10 88\n11 84\n11 82\n12 91\n12 93\n14 89\n;\n<span style=\"color: #800080;\">run<\/span> ;\n\n<span style=\"color: #008000;\">\/*view dataset*\/\n<\/span><span style=\"color: #800080;\">proc print<\/span> <span style=\"color: #3366ff;\">data<\/span> =exam_data;\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-22743 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/simplesas1.jpg\" alt=\"\" width=\"143\" height=\"367\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><b>Ad\u0131m 2: Basit do\u011frusal regresyon modelini yerle\u015ftirin<\/b><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Daha sonra basit do\u011frusal regresyon modeline uyum sa\u011flamak i\u00e7in <strong>proc reg&#8217;i<\/strong> kullanaca\u011f\u0131z:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">\/*fit simple linear regression model*\/\n<\/span><span style=\"color: #800080;\">proc reg<\/span> <span style=\"color: #3366ff;\">data<\/span> =exam_data;\n   <span style=\"color: #3366ff;\">model<\/span> score = hours;\n<span style=\"color: #800080;\">run<\/span> ;<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-22744\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/simplesas2.jpg\" alt=\"SAS'ta basit do\u011frusal regresyon \u00e7\u0131kt\u0131s\u0131\" width=\"416\" height=\"501\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Sonu\u00e7taki her tablodaki en \u00f6nemli de\u011ferleri \u015fu \u015fekilde yorumlayabilirsiniz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Bo\u015fluk analizi tablosu:<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Regresyon modelinin genel <a href=\"https:\/\/statorials.org\/tr\/regresyonda-genel-anlamlilik-icin-f-testini-anlamaya-yonelik-basit-bir-kilavuz\/\" target=\"_blank\" rel=\"noopener\">F de\u011feri<\/a> <strong>63,91&#8217;dir<\/strong> ve kar\u015f\u0131l\u0131k gelen p de\u011feri <strong>&lt;0,0001&#8217;dir<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu p de\u011feri 0,05&#8217;ten k\u00fc\u00e7\u00fck oldu\u011fundan regresyon modelinin bir b\u00fct\u00fcn olarak istatistiksel olarak anlaml\u0131 oldu\u011fu sonucuna var\u0131yoruz. Ba\u015fka bir deyi\u015fle saatler, s\u0131nav sonu\u00e7lar\u0131n\u0131 tahmin etmede faydal\u0131 bir de\u011fi\u015fkendir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Model uyum tablosu:<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">R-Kare de\u011feri bize, \u00e7al\u0131\u015f\u0131lan saat say\u0131s\u0131yla a\u00e7\u0131klanabilecek s\u0131nav puanlar\u0131ndaki de\u011fi\u015fimin y\u00fczdesini verir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Genel olarak, bir regresyon modelinin <a href=\"https:\/\/statorials.org\/tr\/iyi-r-kare-degeri\/\" target=\"_blank\" rel=\"noopener\">R-kare de\u011feri<\/a> ne kadar b\u00fcy\u00fck olursa, yorday\u0131c\u0131 de\u011fi\u015fkenlerin yan\u0131t de\u011fi\u015fkeninin de\u011ferini tahmin etmede o kadar iyi olur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu durumda s\u0131nav puanlar\u0131ndaki farkl\u0131l\u0131\u011f\u0131n <strong>%83,1&#8217;i<\/strong> \u00e7al\u0131\u015f\u0131lan saat say\u0131s\u0131yla a\u00e7\u0131klanabilir. Bu de\u011ferin olduk\u00e7a y\u00fcksek olmas\u0131, \u00e7al\u0131\u015f\u0131lan saatin s\u0131nav sonu\u00e7lar\u0131n\u0131 tahmin etmede olduk\u00e7a faydal\u0131 bir de\u011fi\u015fken oldu\u011funu g\u00f6stermektedir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Parametre tahminleri tablosu:<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu tablodan uygun regresyon denklemini g\u00f6rebiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Puan = 65,33 + 1,98*(saat)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunu, \u00e7al\u0131\u015f\u0131lan her ek saatin s\u0131nav puan\u0131nda ortalama <strong>1,98 puanl\u0131k<\/strong> bir art\u0131\u015fla ili\u015fkili oldu\u011fu \u015feklinde yorumluyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Orijinal de\u011fer bize s\u0131f\u0131r saat ders \u00e7al\u0131\u015fan bir \u00f6\u011frencinin ortalama s\u0131nav puan\u0131n\u0131n <strong>65,33<\/strong> oldu\u011funu s\u00f6yl\u00fcyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu denklemi, \u00f6\u011frencinin ders \u00e7al\u0131\u015ft\u0131\u011f\u0131 saat say\u0131s\u0131na g\u00f6re beklenen s\u0131nav puan\u0131n\u0131 bulmak i\u00e7in de kullanabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin 10 saat ders \u00e7al\u0131\u015fan bir \u00f6\u011frencinin s\u0131nav puan\u0131n\u0131n <strong>85,13<\/strong> olmas\u0131 gerekir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Puan = 65,33 + 1,98*(10) = 85,13<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu tabloda <em>saatlere<\/em> ili\u015fkin p de\u011feri (&lt;0,0001) 0,05&#8217;ten k\u00fc\u00e7\u00fck oldu\u011fundan, bunun istatistiksel olarak anlaml\u0131 bir yorday\u0131c\u0131 de\u011fi\u015fken oldu\u011fu sonucuna var\u0131yoruz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>3. Ad\u0131m: Kalan grafikleri analiz edin<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Basit do\u011frusal regresyon, model <a href=\"https:\/\/statorials.org\/tr\/kalinti\/\" target=\"_blank\" rel=\"noopener\">art\u0131klar\u0131<\/a> hakk\u0131nda iki \u00f6nemli<a href=\"https:\/\/statorials.org\/tr\/dogrusal-regresyon-varsayimlari\/\" target=\"_blank\" rel=\"noopener\">varsay\u0131mda<\/a> bulunur:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Art\u0131klar normal da\u011f\u0131l\u0131ma sahiptir.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Art\u0131klar, yorday\u0131c\u0131 de\u011fi\u015fkenin her seviyesinde e\u015fit varyansa (&#8221; <a href=\"https:\/\/statorials.org\/tr\/degisen-varyans-regresyonu\/\" target=\"_blank\" rel=\"noopener\">e\u015fvaryansl\u0131l\u0131k<\/a> &#8220;) sahiptir.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu varsay\u0131mlar kar\u015f\u0131lanmazsa regresyon modelimizin sonu\u00e7lar\u0131 g\u00fcvenilir olmayabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu varsay\u0131mlar\u0131n kar\u015f\u0131land\u0131\u011f\u0131n\u0131 do\u011frulamak i\u00e7in SAS&#8217;\u0131n \u00e7\u0131kt\u0131da otomatik olarak g\u00f6sterdi\u011fi kalan grafikleri analiz edebiliriz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-22747 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/simplesas3.jpg\" alt=\"\" width=\"663\" height=\"651\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Art\u0131klar\u0131n <strong>normal \u015fekilde da\u011f\u0131ld\u0131\u011f\u0131n\u0131<\/strong> do\u011frulamak i\u00e7in, orta \u00e7izginin sol konumundaki grafi\u011fi, x ekseni boyunca &#8220;Kantil&#8221; ve y ekseni boyunca &#8220;Art\u0131k&#8221; ile analiz edebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu \u00e7izime <a href=\"https:\/\/statorials.org\/tr\/izin-bir-miktar-normalligi\/\" target=\"_blank\" rel=\"noopener\">QQ grafi\u011fi<\/a> denir, &#8220;kantil-nicelik&#8221; kelimesinin k\u0131saltmas\u0131d\u0131r ve verilerin normal \u015fekilde da\u011f\u0131l\u0131p da\u011f\u0131lmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131l\u0131r. Veriler normal olarak da\u011f\u0131l\u0131yorsa, QQ grafi\u011findeki noktalar d\u00fcz bir \u00e7apraz \u00e7izgi \u00fczerinde yer alacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Grafikten noktalar\u0131n kabaca d\u00fcz bir \u00e7apraz \u00e7izgi boyunca uzand\u0131\u011f\u0131n\u0131 g\u00f6rebiliriz, dolay\u0131s\u0131yla art\u0131klar\u0131n normal \u015fekilde da\u011f\u0131ld\u0131\u011f\u0131n\u0131 varsayabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra, art\u0131klar\u0131n <strong>homoskedastik<\/strong> oldu\u011funu do\u011frulamak i\u00e7in, x ekseni boyunca &#8220;Tahmin edilen de\u011fer&#8221; ve y ekseni boyunca &#8220;Art\u0131k&#8221; ile ilk sat\u0131r\u0131n sol konumundaki \u00e7izime bakabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">E\u011fer \u00e7izim noktalar\u0131 net bir model olmadan s\u0131f\u0131r etraf\u0131nda rastgele da\u011f\u0131lm\u0131\u015fsa, o zaman art\u0131klar\u0131n homoskedastic oldu\u011funu varsayabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Grafikten, noktalar\u0131n grafik boyunca her d\u00fczeyde yakla\u015f\u0131k olarak e\u015fit varyansla s\u0131f\u0131r etraf\u0131nda rastgele da\u011f\u0131ld\u0131\u011f\u0131n\u0131 g\u00f6rebiliriz, dolay\u0131s\u0131yla art\u0131klar\u0131n homoskedastik oldu\u011funu varsayabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Her iki varsay\u0131m da kar\u015f\u0131land\u0131\u011f\u0131 i\u00e7in basit do\u011frusal regresyon modelinin sonu\u00e7lar\u0131n\u0131n g\u00fcvenilir oldu\u011funu varsayabiliriz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong><span style=\"color: #000000;\">Ek kaynaklar<\/span><\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimlerde SAS&#8217;ta di\u011fer ortak g\u00f6revlerin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/tek-yonlu-anova-ve-sas\/\" target=\"_blank\" rel=\"noopener\">SAS&#8217;ta tek y\u00f6nl\u00fc ANOVA nas\u0131l ger\u00e7ekle\u015ftirilir?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/hava-kilidinde-iki-seritli-anova\/\" target=\"_blank\" rel=\"noopener\">SAS&#8217;ta iki y\u00f6nl\u00fc ANOVA nas\u0131l ger\u00e7ekle\u015ftirilir?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/hava-kilidindeki-korelasyon\/\" target=\"_blank\" rel=\"noopener\">SAS&#8217;ta korelasyon nas\u0131l hesaplan\u0131r?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Basit do\u011frusal regresyon, yorday\u0131c\u0131 de\u011fi\u015fken ile yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkiyi anlamak i\u00e7in kullanabilece\u011fimiz bir tekniktir. Bu teknik, verilere en iyi &#8220;uyan&#8221; \u00e7izgiyi bulur ve a\u015fa\u011f\u0131daki formu al\u0131r: \u0177 = b 0 + b 1 x Alt\u0131n: \u0177 : Tahmini yan\u0131t de\u011feri b 0 : Regresyon \u00e7izgisinin ba\u015flang\u0131c\u0131 b 1 : Regresyon \u00e7izgisinin e\u011fimi Bu denklem, [&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-2561","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>SAS&#039;ta basit do\u011frusal regresyon nas\u0131l ger\u00e7ekle\u015ftirilir - Statoryaller<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, SAS&#039;ta basit bir do\u011frusal regresyonun nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi eksiksiz bir \u00f6rnekle 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\/sasta-basit-dogrusal-regresyon\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"SAS&#039;ta basit do\u011frusal regresyon nas\u0131l ger\u00e7ekle\u015ftirilir - 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