{"id":1736,"date":"2023-07-25T04:57:36","date_gmt":"2023-07-25T04:57:36","guid":{"rendered":"https:\/\/statorials.org\/tr\/dogrusal-regresyon-icin-sifir-hipotezi\/"},"modified":"2023-07-25T04:57:36","modified_gmt":"2023-07-25T04:57:36","slug":"dogrusal-regresyon-icin-sifir-hipotezi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/dogrusal-regresyon-icin-sifir-hipotezi\/","title":{"rendered":"Do\u011frusal regresyon i\u0307\u00e7in s\u0131f\u0131r hipotezini anlamak"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Do\u011frusal regresyon, bir veya daha fazla yorday\u0131c\u0131 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 anlamak i\u00e7in kullanabilece\u011fimiz bir tekniktir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Yaln\u0131zca bir \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkenimiz ve bir yan\u0131t de\u011fi\u015fkenimiz varsa, de\u011fi\u015fkenler aras\u0131ndaki ili\u015fkiyi tahmin etmek i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanan <a href=\"https:\/\/statorials.org\/tr\/dogrusal-regresyon-1\/\" target=\"_blank\" rel=\"noopener\">basit do\u011frusal regresyonu<\/a> kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0177 = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub> x<\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u0177: Tahmini yan\u0131t de\u011feri.<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u03b2 <sub>0<\/sub> : x s\u0131f\u0131r oldu\u011funda y&#8217;nin ortalama de\u011feri.<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u03b2 <sub>1<\/sub> : x&#8217;teki bir birimlik art\u0131\u015fla ba\u011flant\u0131l\u0131 olarak y&#8217;deki ortalama de\u011fi\u015fiklik.<\/span><\/li>\n<li> <span style=\"color: #000000;\">x: yorday\u0131c\u0131 de\u011fi\u015fkenin de\u011feri.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Basit do\u011frusal regresyon a\u015fa\u011f\u0131daki bo\u015f ve alternatif hipotezleri kullan\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> \u03b2 <sub>1<\/sub> = 0<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>HA<\/sub> :<\/strong> \u03b2 <sub>1<\/sub> \u2260 0<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bo\u015f hipotez, \u03b2 <sub>1<\/sub> katsay\u0131s\u0131n\u0131n s\u0131f\u0131ra e\u015fit oldu\u011funu belirtir. Ba\u015fka bir deyi\u015fle yorday\u0131c\u0131 de\u011fi\u015fken x ile yan\u0131t de\u011fi\u015fkeni y aras\u0131nda istatistiksel olarak anlaml\u0131 bir ili\u015fki yoktur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Alternatif hipotez \u03b2 <sub>1&#8217;in<\/sub> s\u0131f\u0131ra e\u015fit <em>olmad\u0131\u011f\u0131n\u0131<\/em> belirtir. Ba\u015fka bir deyi\u015fle x ile y aras\u0131nda istatistiksel olarak anlaml\u0131 bir ili\u015fki <em>vard\u0131r<\/em> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Birden fazla \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkenimiz ve bir yan\u0131t de\u011fi\u015fkenimiz varsa, de\u011fi\u015fkenler aras\u0131ndaki ili\u015fkiyi tahmin etmek i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanan <a href=\"https:\/\/statorials.org\/tr\/coklu-dogrusal-regresyon\/\" target=\"_blank\" rel=\"noopener\">\u00e7oklu do\u011frusal regresyonu<\/a> kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0177 = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub> x <sub>1<\/sub> + \u03b2 <sub>2<\/sub> x <sub>2<\/sub> + \u2026 + \u03b2 <sub>k<\/sub> x <sub>k<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u0177: Tahmini yan\u0131t de\u011feri.<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u03b2 <sub>0<\/sub> : T\u00fcm yorday\u0131c\u0131 de\u011fi\u015fkenler s\u0131f\u0131ra e\u015fit oldu\u011funda y&#8217;nin ortalama de\u011feri.<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u03b2 <sub>i<\/sub> : <sub>xi&#8217;deki<\/sub> bir birimlik art\u0131\u015fla ba\u011flant\u0131l\u0131 olarak y&#8217;deki ortalama de\u011fi\u015fiklik.<\/span><\/li>\n<li> <span style=\"color: #000000;\">x <sub>i<\/sub> : Tahmin de\u011fi\u015fkeni x <sub>i&#8217;nin<\/sub> de\u011feri.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00c7oklu do\u011frusal regresyon a\u015fa\u011f\u0131daki bo\u015f ve alternatif hipotezleri kullan\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> \u03b2 <sub>1<\/sub> = \u03b2 <sub>2<\/sub> = \u2026 = \u03b2 <sub>k<\/sub> = 0<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>HA<\/sub> :<\/strong> \u03b2 <sub>1<\/sub> = \u03b2 <sub>2<\/sub> = \u2026 = \u03b2 <sub>k<\/sub> \u2260 0<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">S\u0131f\u0131r hipotezi, modeldeki t\u00fcm katsay\u0131lar\u0131n s\u0131f\u0131ra e\u015fit oldu\u011funu belirtir. Ba\u015fka bir deyi\u015fle, yorday\u0131c\u0131 de\u011fi\u015fkenlerden hi\u00e7birinin yan\u0131t de\u011fi\u015fkeni y ile istatistiksel olarak anlaml\u0131 bir ili\u015fkisi yoktur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Alternatif hipotez, t\u00fcm katsay\u0131lar\u0131n ayn\u0131 anda s\u0131f\u0131ra e\u015fit olmad\u0131\u011f\u0131n\u0131 belirtir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler, basit do\u011frusal regresyon ve \u00e7oklu do\u011frusal regresyon modellerinde s\u0131f\u0131r hipotezinin reddedilip reddedilmeyece\u011fine nas\u0131l karar verilece\u011fini g\u00f6sterir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: Basit do\u011frusal regresyon<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir profes\u00f6r\u00fcn, s\u0131n\u0131f\u0131ndaki \u00f6\u011frencilerin alaca\u011f\u0131 s\u0131nav notunu tahmin etmek i\u00e7in \u00e7al\u0131\u015f\u0131lan saat say\u0131s\u0131n\u0131 kullanmak istedi\u011fini varsayal\u0131m. 20 \u00f6\u011frenciden veri topluyor ve basit bir do\u011frusal regresyon modeline uyuyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki ekran g\u00f6r\u00fcnt\u00fcs\u00fc regresyon modelinin sonucunu g\u00f6stermektedir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/simpleregressionexcel5.png\" alt=\"Excel'de Basit Do\u011frusal Regresyon \u00c7\u0131kt\u0131s\u0131\" width=\"665\" height=\"370\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Uygun basit do\u011frusal regresyon modeli:<\/span><\/p>\n<p> <span style=\"color: #000000;\">S\u0131nav puan\u0131 = 67.1617 + 5.2503*(\u00e7al\u0131\u015f\u0131lan saat)<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00c7al\u0131\u015f\u0131lan saat ile s\u0131nav puan\u0131 aras\u0131nda istatistiksel olarak anlaml\u0131 bir ili\u015fki olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in modelin <a href=\"https:\/\/statorials.org\/tr\/regresyonda-genel-anlamlilik-icin-f-testini-anlamaya-yonelik-basit-bir-kilavuz\/\" target=\"_blank\" rel=\"noopener\">genel F de\u011ferini<\/a> ve buna kar\u015f\u0131l\u0131k gelen p de\u011ferini analiz etmemiz gerekir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Genel F de\u011feri: <strong>47,9952<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">P de\u011feri: <strong>0,000<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu p de\u011feri 0,05&#8217;ten k\u00fc\u00e7\u00fck oldu\u011fundan s\u0131f\u0131r hipotezini reddedebiliriz. Yani ders \u00e7al\u0131\u015f\u0131lan saat ile s\u0131nav puanlar\u0131 aras\u0131nda istatistiksel olarak anlaml\u0131 bir ili\u015fki vard\u0131r.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: \u00c7oklu do\u011frusal regresyon<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir profes\u00f6r\u00fcn, \u00f6\u011frencilerinin s\u0131n\u0131f\u0131nda kazanaca\u011f\u0131 notu tahmin etmek i\u00e7in \u00e7al\u0131\u015f\u0131lan saat say\u0131s\u0131n\u0131 ve girilen haz\u0131rl\u0131k s\u0131navlar\u0131n\u0131n say\u0131s\u0131n\u0131 kullanmak istedi\u011fini varsayal\u0131m. 20 \u00f6\u011frenciden veri topluyor ve \u00e7oklu do\u011frusal regresyon modeline uyuyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki ekran g\u00f6r\u00fcnt\u00fcs\u00fc regresyon modelinin sonucunu g\u00f6stermektedir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/multipleregexcel4.png\" alt=\"Excel'de \u00c7oklu Do\u011frusal Regresyon \u00c7\u0131kt\u0131s\u0131\" width=\"570\" height=\"394\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Uygun \u00e7oklu do\u011frusal regresyon modeli:<\/span><\/p>\n<p> <span style=\"color: #000000;\">S\u0131nav puan\u0131 = 67,67 + 5,56*(\u00e7al\u0131\u015f\u0131lan saat) \u2013 0,60*(girilen haz\u0131rl\u0131k s\u0131navlar\u0131)<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130ki yorday\u0131c\u0131 de\u011fi\u015fken ile yan\u0131t de\u011fi\u015fkeni aras\u0131nda istatistiksel olarak anlaml\u0131 bir ili\u015fki olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in modelin genel F de\u011ferini ve buna kar\u015f\u0131l\u0131k gelen p de\u011ferini analiz etmemiz gerekir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Genel F de\u011feri: <strong>23,46<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">P de\u011feri: <strong>0,00<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu p de\u011feri 0,05&#8217;ten k\u00fc\u00e7\u00fck oldu\u011fundan s\u0131f\u0131r hipotezini reddedebiliriz. Ba\u015fka bir deyi\u015fle, \u00e7al\u0131\u015f\u0131lan saatlerin ve girilen haz\u0131rl\u0131k s\u0131navlar\u0131n\u0131n s\u0131nav sonu\u00e7lar\u0131yla istatistiksel olarak anlaml\u0131 bir ili\u015fkisi vard\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Not:<\/strong> Girilen haz\u0131rl\u0131k s\u0131navlar\u0131n\u0131n p de\u011feri (p = 0,52) anlaml\u0131 olmasa da, haz\u0131rl\u0131k s\u0131navlar\u0131 ile \u00e7al\u0131\u015f\u0131lan saatlerin <em>birle\u015fimi<\/em> s\u0131nav sonu\u00e7lar\u0131yla anlaml\u0131 bir ili\u015fkiye sahiptir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/tr\/regresyonda-genel-anlamlilik-icin-f-testini-anlamaya-yonelik-basit-bir-kilavuz\/\" target=\"_blank\" rel=\"noopener\">Regresyonda Genel \u00d6nem i\u00e7in F Testini Anlamak<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/regresyon-yorumlama-tablosunu-okuyun\/\" target=\"_blank\" rel=\"noopener\">Regresyon Tablosu Nas\u0131l Okunmal\u0131 ve Yorumlanmal\u0131<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/regresyon-sonuclari-nasil-raporlanir\/\" target=\"_blank\" rel=\"noopener\">Regresyon sonu\u00e7lar\u0131 nas\u0131l raporlan\u0131r?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/basit-dogrusal-regresyon-excel\/\" target=\"_blank\" rel=\"noopener\">Excel&#8217;de basit do\u011frusal regresyon nas\u0131l ger\u00e7ekle\u015ftirilir<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/coklu-dogrusal-regresyon-excel\/\" target=\"_blank\" rel=\"noopener\">Excel&#8217;de \u00e7oklu do\u011frusal regresyon nas\u0131l ger\u00e7ekle\u015ftirilir<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Do\u011frusal regresyon, bir veya daha fazla yorday\u0131c\u0131 de\u011fi\u015fken ile bir yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkiyi anlamak i\u00e7in kullanabilece\u011fimiz bir tekniktir. Yaln\u0131zca bir \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkenimiz ve bir yan\u0131t de\u011fi\u015fkenimiz varsa, de\u011fi\u015fkenler aras\u0131ndaki ili\u015fkiyi tahmin etmek i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanan basit do\u011frusal regresyonu kullanabiliriz: \u0177 = \u03b2 0 + \u03b2 1 x Alt\u0131n: \u0177: Tahmini yan\u0131t de\u011feri. \u03b2 [&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-1736","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>Do\u011frusal Regresyon \u0130\u00e7in S\u0131f\u0131r Hipotezini Anlamak<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde \u00f6rnekler de dahil 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