{"id":1446,"date":"2023-07-26T08:50:26","date_gmt":"2023-07-26T08:50:26","guid":{"rendered":"https:\/\/statorials.org\/tr\/rde-ustel-regresyon\/"},"modified":"2023-07-26T08:50:26","modified_gmt":"2023-07-26T08:50:26","slug":"rde-ustel-regresyon","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/rde-ustel-regresyon\/","title":{"rendered":"R&#39;de \u00fcstel regresyon (ad\u0131m ad\u0131m)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>\u00dcstel regresyon,<\/strong> a\u015fa\u011f\u0131daki durumlar\u0131 modellemek i\u00e7in kullan\u0131labilecek bir regresyon t\u00fcr\u00fcd\u00fcr:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. \u00dcstel B\u00fcy\u00fcme:<\/strong> B\u00fcy\u00fcme yava\u015f ba\u015flar, daha sonra h\u0131zl\u0131 ve s\u0131n\u0131rs\u0131z bir \u015fekilde h\u0131zlan\u0131r.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14288 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/expregexcel1.png\" alt=\"\" width=\"329\" height=\"244\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. \u00dcstel bozunma:<\/strong> Bozunma h\u0131zla ba\u015flar ve sonra yava\u015flayarak s\u0131f\u0131ra yakla\u015f\u0131r.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14289 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/expregexcel2.png\" alt=\"\" width=\"332\" height=\"251\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u00dcstel regresyon modelinin denklemi a\u015fa\u011f\u0131daki formu al\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">y = <sup>abx<\/sup><\/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:<\/strong> tahmin de\u011fi\u015fkeni<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>a, b:<\/strong> <em>x<\/em> ve <em>y<\/em> aras\u0131ndaki ili\u015fkiyi tan\u0131mlayan regresyon katsay\u0131lar\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki ad\u0131m ad\u0131m \u00f6rnek, R&#8217;de \u00fcstel regresyonun nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini g\u00f6sterir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>1. Ad\u0131m: Verileri olu\u015fturun<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u00d6ncelikle iki de\u011fi\u015fken i\u00e7in sahte veriler olu\u015ftural\u0131m: <em>x<\/em> ve <em>y<\/em> :<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong>x=1:20\ny=c(1, 3, 5, 7, 9, 12, 15, 19, 23, 28, 33, 38, 44, 50, 56, 64, 73, 84, 97, 113)\n<\/strong><\/pre>\n<h3> <strong>2. Ad\u0131m: Verileri g\u00f6rselle\u015ftirin<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">\u015eimdi <em>x<\/em> ile <em>y<\/em> aras\u0131ndaki ili\u015fkiyi g\u00f6rselle\u015ftirmek i\u00e7in h\u0131zl\u0131 bir da\u011f\u0131l\u0131m grafi\u011fi olu\u015ftural\u0131m:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong>plot(x, y)<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14298\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/expregr1.png\" alt=\"R'de \u00fcstel regresyon \u00f6rne\u011fi\" width=\"419\" height=\"376\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Grafikten iki de\u011fi\u015fken aras\u0131nda net bir \u00fcstel b\u00fcy\u00fcme modelinin oldu\u011funu g\u00f6rebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu nedenle de\u011fi\u015fkenler aras\u0131ndaki ili\u015fkiyi tan\u0131mlamak i\u00e7in \u00fcstel bir regresyon denklemi uydurmak ak\u0131ll\u0131ca g\u00f6r\u00fcnmektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ad\u0131m 3: \u00dcstel regresyon modelini yerle\u015ftirin<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Daha sonra, <a href=\"https:\/\/statorials.org\/tr\/degiskenleri-aciklayici-yanitlar\/\" target=\"_blank\" rel=\"noopener\">yan\u0131t de\u011fi\u015fkeni<\/a> olarak <em>y&#8217;nin<\/em> ve tahmin de\u011fi\u015fkeni olarak <em>x&#8217;in<\/em> do\u011fal logaritmas\u0131n\u0131 kullanarak \u00fcstel bir regresyon modeline uyum sa\u011flamak i\u00e7in <strong>lm()<\/strong> i\u015flevini kullanaca\u011f\u0131z:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#fit the model<\/span>\nmodel &lt;- lm( <span style=\"color: #3366ff;\">log<\/span> (y) ~ x)<\/strong>\n<strong>\n<span style=\"color: #008080;\">#view the output of the model<\/span>\nsummary(model)\n\nCall:\nlm(formula = log(y) ~ x)\n\nResiduals:\n    Min 1Q Median 3Q Max \n-1.1858 -0.1768 0.1104 0.2720 0.3300 \n\nCoefficients:\n            Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) 0.98166 0.17118 5.735 1.95e-05 ***\nx 0.20410 0.01429 14.283 2.92e-11 ***\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 0.3685 on 18 degrees of freedom\nMultiple R-squared: 0.9189, Adjusted R-squared: 0.9144 \nF-statistic: 204 on 1 and 18 DF, p-value: 2.917e-11<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">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\u011feri<\/a> 204&#8217;t\u00fcr ve buna kar\u015f\u0131l\u0131k gelen p de\u011feri son derece d\u00fc\u015f\u00fckt\u00fcr (2,917e-11), bu da modelin bir b\u00fct\u00fcn olarak faydal\u0131 oldu\u011funu g\u00f6stermektedir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00c7\u0131kt\u0131 tablosundaki katsay\u0131lar\u0131 kullanarak, uygun \u00fcstel regresyon denkleminin \u015f\u00f6yle oldu\u011funu g\u00f6rebiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>ln(y) = 0,9817 + 0,2041(x)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Her iki tarafa da <em>e<\/em> uyguland\u0131\u011f\u0131nda denklemi a\u015fa\u011f\u0131daki gibi yeniden yazabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>y = 2,6689 * <sup>1,2264x<\/sup><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu denklemi, tahmin de\u011fi\u015fkeni <em>x&#8217;in<\/em> de\u011ferine dayanarak yan\u0131t de\u011fi\u015fkeni <em>y&#8217;yi<\/em> tahmin etmek i\u00e7in kullanabiliriz.<\/span> <span style=\"color: #000000;\">\u00d6rne\u011fin, <em>x<\/em> = 12 ise <em>y&#8217;nin<\/em> <strong>30,897<\/strong> olaca\u011f\u0131n\u0131 tahmin ederiz:<\/span><\/p>\n<p> <span style=\"color: #000000;\">y = 2,6689 * 1,2264 <sup>12<\/sup> = 30,897<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Bonus:<\/strong> Belirli bir tahminci ve yan\u0131t de\u011fi\u015fkeni i\u00e7in \u00fcstel regresyon denklemini otomatik olarak hesaplamak i\u00e7in bu \u00e7evrimi\u00e7i \u00fcstel regresyon hesaplay\u0131c\u0131s\u0131n\u0131 kullanmaktan \u00e7ekinmeyin.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/tr\/rde-basit-dogrusal-regresyon\/\" target=\"_blank\" rel=\"noopener\">R&#8217;de basit do\u011frusal regresyon nas\u0131l ger\u00e7ekle\u015ftirilir<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/coklu-dogrusal-regresyon-r\/\" target=\"_blank\" rel=\"noopener\">R&#8217;de \u00e7oklu do\u011frusal regresyon nas\u0131l ger\u00e7ekle\u015ftirilir<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/ikinci-dereceden-regresyon-r\/\" target=\"_blank\" rel=\"noopener\">R&#8217;de ikinci dereceden regresyon nas\u0131l ger\u00e7ekle\u015ftirilir?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/polinom-regresyon-r\/\" target=\"_blank\" rel=\"noopener\">R&#8217;de polinom regresyonu nas\u0131l ger\u00e7ekle\u015ftirilir<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00dcstel regresyon, a\u015fa\u011f\u0131daki durumlar\u0131 modellemek i\u00e7in kullan\u0131labilecek bir regresyon t\u00fcr\u00fcd\u00fcr: 1. \u00dcstel B\u00fcy\u00fcme: B\u00fcy\u00fcme yava\u015f ba\u015flar, daha sonra h\u0131zl\u0131 ve s\u0131n\u0131rs\u0131z bir \u015fekilde h\u0131zlan\u0131r. 2. \u00dcstel bozunma: Bozunma h\u0131zla ba\u015flar ve sonra yava\u015flayarak s\u0131f\u0131ra yakla\u015f\u0131r. \u00dcstel regresyon modelinin denklemi a\u015fa\u011f\u0131daki formu al\u0131r: y = abx Alt\u0131n: y: yan\u0131t de\u011fi\u015fkeni x: tahmin de\u011fi\u015fkeni a, b: x [&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-1446","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - 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