{"id":2243,"date":"2023-07-23T02:52:08","date_gmt":"2023-07-23T02:52:08","guid":{"rendered":"https:\/\/statorials.org\/tr\/lojistik-regresyonun-bos-hipotezi\/"},"modified":"2023-07-23T02:52:08","modified_gmt":"2023-07-23T02:52:08","slug":"lojistik-regresyonun-bos-hipotezi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/lojistik-regresyonun-bos-hipotezi\/","title":{"rendered":"Lojistik regresyon i\u0307\u00e7in s\u0131f\u0131r hipotezini anlamak"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/lojistik-regresyon-1\/\" target=\"_blank\" rel=\"noopener\">Lojistik regresyon,<\/a> yan\u0131t de\u011fi\u015fkeni ikili oldu\u011funda 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 regresyon modeli t\u00fcr\u00fcd\u00fcr.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Yaln\u0131zca bir yorday\u0131c\u0131 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 <strong>basit lojistik regresyonu<\/strong> kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>log[p(X) \/ (1-p(X))] = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Denklemin sa\u011f taraf\u0131ndaki form\u00fcl, yan\u0131t de\u011fi\u015fkeninin 1 de\u011ferini alma ihtimalinin logaritmas\u0131n\u0131 tahmin eder.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Basit lojistik 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 yorday\u0131c\u0131 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 <strong>\u00e7oklu lojistik regresyonu<\/strong> kullanabiliriz:<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">log[p(X) \/ (1-p(X))] = \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><\/strong><\/p>\n<p> <span style=\"color: #000000;\">\u00c7oklu lojistik 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 lojistik regresyon ve \u00e7oklu lojistik 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 lojistik 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 lojistik regresyon modeline uyuyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Basit bir lojistik regresyon modeline uymak i\u00e7in R&#8217;de a\u015fa\u011f\u0131daki kodu kullanabiliriz:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#createdata\n<\/span>df &lt;- data. <span style=\"color: #3366ff;\">frame<\/span> (result=c(0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1),\n                 hours=c(1, 5, 5, 1, 2, 1, 3, 2, 2, 1, 2, 1, 3, 4, 4, 2, 1, 1, 4, 3))\n\n<span style=\"color: #008080;\">#fit simple logistic regression model\n<\/span>model &lt;- glm(result~hours, family=' <span style=\"color: #ff0000;\">binomial<\/span> ', data=df)\n\n<span style=\"color: #008080;\">#view summary of model fit\n<\/span>summary(model)\n\nCall:\nglm(formula = result ~ hours, family = \"binomial\", data = df)\n\nDeviance Residuals: \n    Min 1Q Median 3Q Max  \n-1.8244 -1.1738 0.7701 0.9460 1.2236  \n\nCoefficients:\n            Estimate Std. Error z value Pr(&gt;|z|)\n(Intercept) -0.4987 0.9490 -0.526 0.599\nhours 0.3906 0.3714 1.052 0.293\n\n(Dispersion parameter for binomial family taken to be 1)\n\n    Null deviance: 26,920 on 19 degrees of freedom\nResidual deviance: 25,712 on 18 degrees of freedom\nAIC: 29,712\n\nNumber of Fisher Scoring iterations: 4\n\n<span style=\"color: #008080;\">#calculate p-value of overall Chi-Square statistic\n<\/span>1-pchisq(26.920-25.712, 19-18)\n\n[1] 0.2717286\n<\/strong><\/pre>\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 genel ki-kare de\u011ferini ve buna kar\u015f\u0131l\u0131k gelen p de\u011ferini analiz etmemiz gerekir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Modelin genel ki-kare de\u011ferini hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\">X <sup>2<\/sup> = (S\u0131f\u0131r sapma \u2013 Art\u0131k sapma) \/ (S\u0131f\u0131r Df \u2013 Art\u0131k sapma)<\/span><\/p>\n<p> <span style=\"color: #000000;\">P de\u011feri <strong>0,2717286<\/strong> olarak \u00e7\u0131k\u0131yor.<\/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. Yani \u00e7al\u0131\u015f\u0131lan saat ile s\u0131nav puanlar\u0131 aras\u0131nda istatistiksel olarak anlaml\u0131 bir ili\u015fki bulunmamaktad\u0131r.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: \u00c7oklu lojistik 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 girdi\u011fi haz\u0131rl\u0131k s\u0131navlar\u0131n\u0131n say\u0131s\u0131n\u0131 kullanmak istedi\u011fini varsayal\u0131m. 20 \u00f6\u011frenciden veri topluyor ve \u00e7oklu lojistik regresyon modeline uyuyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00c7oklu lojistik regresyon modeline uymak i\u00e7in R&#8217;de a\u015fa\u011f\u0131daki kodu kullanabiliriz:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create data\n<\/span>df &lt;- data. <span style=\"color: #3366ff;\">frame<\/span> (result=c(0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1),\n                 hours=c(1, 5, 5, 1, 2, 1, 3, 2, 2, 1, 2, 1, 3, 4, 4, 2, 1, 1, 4, 3),\n                 exams=c(1, 2, 2, 1, 2, 1, 1, 3, 2, 4, 3, 2, 2, 4, 4, 5, 4, 4, 3, 5))\n\n<span style=\"color: #008080;\">#fit simple logistic regression model\n<\/span>model &lt;- glm(result~hours+exams, family=' <span style=\"color: #ff0000;\">binomial<\/span> ', data=df)\n\n<span style=\"color: #008080;\">#view summary of model fit\n<\/span>summary(model)\n\nCall:\nglm(formula = result ~ hours + exams, family = \"binomial\", data = df)\n\nDeviance Residuals: \n    Min 1Q Median 3Q Max  \n-1.5061 -0.6395 0.3347 0.6300 1.7014  \n\nCoefficients:\n            Estimate Std. Error z value Pr(&gt;|z|)  \n(Intercept) -3.4873 1.8557 -1.879 0.0602 .\nhours 0.3844 0.4145 0.927 0.3538  \nexams 1.1549 0.5493 2.103 0.0355 *\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\n(Dispersion parameter for binomial family taken to be 1)\n\n    Null deviance: 26,920 on 19 degrees of freedom\nResidual deviance: 19,067 on 17 degrees of freedom\nAIC: 25,067\n\nNumber of Fisher Scoring iterations: 5\n\n<span style=\"color: #008080;\">#calculate p-value of overall Chi-Square statistic\n<\/span>1-pchisq(26.920-19.067, 19-17)\n\n[1] 0.01971255\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Modelin genel ki-kare istatisti\u011finin p de\u011feri <strong>0,01971255<\/strong> olarak \u00e7\u0131k\u0131yor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu p de\u011feri 0,05&#8217;ten k\u00fc\u00e7\u00fck oldu\u011fundan s\u0131f\u0131r hipotezini reddediyoruz. Ba\u015fka bir deyi\u015fle, \u00e7al\u0131\u015f\u0131lan saat ve al\u0131nan haz\u0131rl\u0131k s\u0131navlar\u0131n\u0131n kombinasyonu ile s\u0131navdan al\u0131nan final notu aras\u0131nda istatistiksel olarak anlaml\u0131 bir ili\u015fki vard\u0131r.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimler lojistik regresyon hakk\u0131nda ek bilgi sa\u011flar:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/lojistik-regresyon-1\/\" target=\"_blank\" rel=\"noopener\">Lojistik Regresyona Giri\u015f<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/lojistik-regresyon-sonuclari-nasil-raporlanir\/\" target=\"_blank\" rel=\"noopener\">Lojistik regresyon sonu\u00e7lar\u0131 nas\u0131l raporlan\u0131r?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/lojistik-regresyon-ve-dogrusal-regresyon\/\" target=\"_blank\" rel=\"noopener\">Lojistik regresyon ve do\u011frusal regresyon: temel farklar<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Lojistik regresyon, yan\u0131t de\u011fi\u015fkeni ikili oldu\u011funda 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 regresyon modeli t\u00fcr\u00fcd\u00fcr. Yaln\u0131zca bir yorday\u0131c\u0131 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 lojistik regresyonu kullanabiliriz: log[p(X) \/ (1-p(X))] = \u03b2 0 + \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-2243","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>Lojistik Regresyon \u0130\u00e7in S\u0131f\u0131r Hipotezini Anlamak - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde lojistik regresyon i\u00e7in s\u0131f\u0131r hipotezi birka\u00e7 \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\/lojistik-regresyonun-bos-hipotezi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Lojistik Regresyon \u0130\u00e7in S\u0131f\u0131r Hipotezini Anlamak - 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