{"id":1151,"date":"2023-07-27T12:05:11","date_gmt":"2023-07-27T12:05:11","guid":{"rendered":"https:\/\/statorials.org\/tr\/rde-basit-dogrusal-regresyon\/"},"modified":"2023-07-27T12:05:11","modified_gmt":"2023-07-27T12:05:11","slug":"rde-basit-dogrusal-regresyon","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/rde-basit-dogrusal-regresyon\/","title":{"rendered":"R&#39;de basit do\u011frusal regresyon nas\u0131l ger\u00e7ekle\u015ftirilir (ad\u0131m ad\u0131m)"},"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> tek bir <a href=\"https:\/\/statorials.org\/tr\/degiskenleri-aciklayici-yanitlar\/\" target=\"_blank\" rel=\"noopener noreferrer\">a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fken<\/a> ile tek bir <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;\">\u00d6zetle, 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 a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fken ile yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkiyi anlamam\u0131za yard\u0131mc\u0131 olabilir ve (istatistiksel olarak anlaml\u0131 oldu\u011fu varsay\u0131larak) a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenin de\u011feri g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda bir yan\u0131t de\u011fi\u015fkeninin de\u011ferini tahmin etmek i\u00e7in kullan\u0131labilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu e\u011fitim, R&#8217;de basit do\u011frusal regresyonun nas\u0131l ger\u00e7ekle\u015ftirilece\u011fine ili\u015fkin ad\u0131m ad\u0131m bir a\u00e7\u0131klama sa\u011flar.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><b>1. Ad\u0131m: Verileri y\u00fckleyin<\/b><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte 15 \u00f6\u011frenci i\u00e7in a\u015fa\u011f\u0131daki iki de\u011fi\u015fkeni i\u00e7eren sahte bir veri seti olu\u015fturaca\u011f\u0131z:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Belirli s\u0131navlar i\u00e7in \u00e7al\u0131\u015f\u0131lan toplam saat say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\">S\u0131nav sonucu<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fken olarak <em>saatleri<\/em> ve yan\u0131t de\u011fi\u015fkeni olarak <em>muayene sonu\u00e7lar\u0131n\u0131<\/em> kullanarak basit bir do\u011frusal regresyon modeli uydurmaya \u00e7al\u0131\u015faca\u011f\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, bu sahte veri k\u00fcmesinin R&#8217;de nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create dataset<\/span>\ndf &lt;- data.frame(hours=c(1, 2, 4, 5, 5, 6, 6, 7, 8, 10, 11, 11, 12, 12, 14),\n                 score=c(64, 66, 76, 73, 74, 81, 83, 82, 80, 88, 84, 82, 91, 93, 89))\n\n<span style=\"color: #008080;\">#view first six rows of dataset\n<\/span>head(df)\n\n  hours score\n1 1 64\n2 2 66\n3 4 76\n4 5 73\n5 5 74\n6 6 81\n\n<span style=\"color: #008080;\">#attach dataset to make it more convenient to work with\n<\/span>attach(df)\n<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><b>2. Ad\u0131m: Verileri g\u00f6rselle\u015ftirin<\/b><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Basit bir do\u011frusal regresyon modeli kurmadan \u00f6nce, anlamak i\u00e7in \u00f6ncelikle verileri g\u00f6rselle\u015ftirmemiz gerekir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130lk olarak, <em>saat<\/em> ve <em>puan<\/em> aras\u0131ndaki ili\u015fkinin yakla\u015f\u0131k olarak do\u011frusal oldu\u011fundan emin olmak istiyoruz \u00e7\u00fcnk\u00fc bu, basit do\u011frusal regresyonun <a href=\"https:\/\/statorials.org\/tr\/dogrusal-regresyon-varsayimlari\/\" target=\"_blank\" rel=\"noopener noreferrer\">temelinde yatan<\/a> \u00e7ok b\u00fcy\u00fck bir varsay\u0131md\u0131r. \u0130ki de\u011fi\u015fken aras\u0131ndaki ili\u015fkiyi g\u00f6rselle\u015ftirmek i\u00e7in basit bir da\u011f\u0131l\u0131m grafi\u011fi olu\u015fturabiliriz:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong>scatter.smooth(hours, score, main=' <span style=\"color: #008000;\">Hours studied vs. Exam Score<\/span> ')\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11531 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/simpleregr1.png\" alt=\"R'de basit do\u011frusal regresyon i\u00e7in da\u011f\u0131l\u0131m grafi\u011fi\" width=\"390\" height=\"384\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Grafikten ili\u015fkinin do\u011frusal oldu\u011funu g\u00f6rebiliriz. <em>Saat say\u0131s\u0131<\/em> artt\u0131k\u00e7a <em>puan<\/em> da do\u011frusal olarak artma e\u011filimindedir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra s\u0131nav sonu\u00e7lar\u0131n\u0131n da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6rselle\u015ftirmek ve <a href=\"https:\/\/statorials.org\/tr\/aykiri-degerleri-kaldir-r\/\" target=\"_blank\" rel=\"noopener noreferrer\">ayk\u0131r\u0131 de\u011ferleri<\/a> kontrol etmek i\u00e7in bir kutu grafi\u011fi olu\u015fturabiliriz. Varsay\u0131lan olarak R, bir g\u00f6zlemi, \u00fc\u00e7\u00fcnc\u00fc \u00e7eyre\u011fin (Q3) \u00e7eyrekler aras\u0131 aral\u0131\u011f\u0131n 1,5 kat\u0131 \u00fczerinde veya ilk \u00e7eyre\u011fin (Q1) alt\u0131ndaki \u00e7eyrekler aras\u0131 aral\u0131\u011f\u0131n 1,5 kat\u0131 olmas\u0131 durumunda ayk\u0131r\u0131 de\u011fer olarak tan\u0131mlar.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir g\u00f6zlem ayk\u0131r\u0131 ise kutu grafi\u011finde k\u00fc\u00e7\u00fck bir daire g\u00f6r\u00fcnecektir:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong>boxplot(score)<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11532 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/simpleregr2.png\" alt=\"R'de basit do\u011frusal regresyon i\u00e7in kutu grafi\u011fi\" width=\"410\" height=\"343\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Kutu grafi\u011finde k\u00fc\u00e7\u00fck daireler yok, bu da veri setimizde ayk\u0131r\u0131 de\u011ferlerin olmad\u0131\u011f\u0131 anlam\u0131na geliyor.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><b>Ad\u0131m 3: Basit Do\u011frusal Regresyon Ger\u00e7ekle\u015ftirin<\/b><\/span><\/h3>\n<p> <span style=\"color: #000000;\">De\u011fi\u015fkenlerimiz aras\u0131ndaki ili\u015fkinin do\u011frusal oldu\u011funu ve ayk\u0131r\u0131 de\u011ferlerin olmad\u0131\u011f\u0131n\u0131 do\u011frulad\u0131ktan sonra, a\u00e7\u0131klay\u0131c\u0131 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 uydurmaya devam edebiliriz:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#fit simple linear regression model\n<\/span>model &lt;- lm(score~hours)\n\n<span style=\"color: #008080;\">#view model summary<\/span>\nsummary(model)\n\nCall:\nlm(formula = score ~ hours)\n\nResiduals:\n   Min 1Q Median 3Q Max \n-5,140 -3,219 -1,193 2,816 5,772 \n\nCoefficients:\n            Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) 65,334 2,106 31,023 1.41e-13 ***\nhours 1.982 0.248 7.995 2.25e-06 ***\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 3.641 on 13 degrees of freedom\nMultiple R-squared: 0.831, Adjusted R-squared: 0.818 \nF-statistic: 63.91 on 1 and 13 DF, p-value: 2.253e-06\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Model \u00f6zetinden uygun regresyon denkleminin \u015f\u00f6yle oldu\u011funu g\u00f6rebiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Puan = 65,334 + 1,982*(saat)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu, \u00e7al\u0131\u015f\u0131lan her ek saatin ortalama <strong>1.982<\/strong> puanl\u0131k s\u0131nav puan\u0131 art\u0131\u015f\u0131yla ili\u015fkili oldu\u011fu anlam\u0131na gelir. Ve <strong>65.334&#8217;\u00fcn<\/strong> orijinal de\u011feri bize s\u0131f\u0131r saat ders \u00e7al\u0131\u015fan bir \u00f6\u011frencinin ortalama beklenen s\u0131nav puan\u0131n\u0131 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. \u00d6rne\u011fin 10 saat ders \u00e7al\u0131\u015fan bir \u00f6\u011frencinin s\u0131nav puan\u0131n\u0131n <strong>85,15<\/strong> olmas\u0131 gerekir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Puan = 65,334 + 1,982*(10) = 85,15<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Model \u00f6zetinin geri kalan\u0131n\u0131 \u015fu \u015fekilde yorumlayabilirsiniz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Pr(&gt;|t|):<\/strong> Model katsay\u0131lar\u0131yla ili\u015fkili p de\u011feridir. <em>Saatlere<\/em> ili\u015fkin p de\u011feri (2,25e-06) 0,05&#8217;ten anlaml\u0131 derecede k\u00fc\u00e7\u00fck oldu\u011fundan <em>saat<\/em> ile <em>puan<\/em> aras\u0131nda istatistiksel olarak anlaml\u0131 bir ili\u015fkinin oldu\u011funu s\u00f6yleyebiliriz.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u00c7oklu R-kare:<\/strong> Bu say\u0131 bize s\u0131nav puanlar\u0131ndaki de\u011fi\u015fim y\u00fczdesinin \u00e7al\u0131\u015f\u0131lan saat say\u0131s\u0131yla a\u00e7\u0131klanabilece\u011fini s\u00f6yler. Genel olarak, bir regresyon modelinin R-kare de\u011feri ne kadar b\u00fcy\u00fck olursa, a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenler yan\u0131t de\u011fi\u015fkeninin de\u011ferini o kadar iyi tahmin edebilir. Bu durumda puanlardaki de\u011fi\u015fimin <strong>%83,1&#8217;i<\/strong> \u00e7al\u0131\u015f\u0131lan saatlerle a\u00e7\u0131klanabilir.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Art\u0131k standart hata:<\/strong> g\u00f6zlenen de\u011ferler ile regresyon \u00e7izgisi aras\u0131ndaki ortalama mesafedir. Bu de\u011fer ne kadar d\u00fc\u015f\u00fck olursa, bir regresyon \u00e7izgisinin g\u00f6zlemlenen verilere o kadar fazla kar\u015f\u0131l\u0131k gelebilmesi m\u00fcmk\u00fcnd\u00fcr. Bu durumda s\u0131navda g\u00f6zlemlenen ortalama puan, regresyon \u00e7izgisinin \u00f6ng\u00f6rd\u00fc\u011f\u00fc puandan <strong>3.641<\/strong> puan sapmaktad\u0131r.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>F istatisti\u011fi ve p de\u011feri:<\/strong> F istatisti\u011fi ( <strong>63.91<\/strong> ) ve kar\u015f\u0131l\u0131k gelen p de\u011feri ( <strong>2.253e-06<\/strong> ) bize regresyon modelinin genel \u00f6nemini, yani modeldeki a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenlerin varyasyonu a\u00e7\u0131klamakta yararl\u0131 olup olmad\u0131\u011f\u0131n\u0131 anlat\u0131r. . yan\u0131t de\u011fi\u015fkeninde. Bu \u00f6rnekteki p de\u011feri 0,05&#8217;ten k\u00fc\u00e7\u00fck oldu\u011fundan modelimiz istatistiksel olarak anlaml\u0131d\u0131r ve <em>saatlerin<\/em> <em>puan<\/em> de\u011fi\u015fimini a\u00e7\u0131klamada faydal\u0131 oldu\u011fu d\u00fc\u015f\u00fcn\u00fclmektedir.<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>Ad\u0131m 4: Art\u0131k Grafikler Olu\u015fturun<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Basit do\u011frusal regresyon modelini verilere yerle\u015ftirdikten sonra son ad\u0131m, art\u0131k grafiklerin olu\u015fturulmas\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Do\u011frusal regresyonun temel varsay\u0131mlar\u0131ndan biri, bir regresyon modelinin art\u0131klar\u0131n\u0131n yakla\u015f\u0131k olarak normal da\u011f\u0131ld\u0131\u011f\u0131 ve a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenin her seviyesinde <a href=\"https:\/\/statorials.org\/tr\/degisen-varyans-regresyonu\/\" target=\"_blank\" rel=\"noopener noreferrer\">homoskedastik<\/a> oldu\u011fudur. Bu varsay\u0131mlar\u0131n kar\u015f\u0131lanmamas\u0131 halinde regresyon modelimizin sonu\u00e7lar\u0131 yan\u0131lt\u0131c\u0131 veya g\u00fcvenilmez olabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu varsay\u0131mlar\u0131n kar\u015f\u0131land\u0131\u011f\u0131n\u0131 do\u011frulamak i\u00e7in a\u015fa\u011f\u0131daki kalan grafikleri olu\u015fturabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Art\u0131klar\u0131n ve uydurulmu\u015f de\u011ferlerin grafi\u011fi:<\/strong> Bu grafik, e\u015f varyansl\u0131l\u0131\u011f\u0131n do\u011frulanmas\u0131 i\u00e7in kullan\u0131\u015fl\u0131d\u0131r. X ekseni tak\u0131lan de\u011ferleri, y ekseni ise art\u0131klar\u0131 g\u00f6r\u00fcnt\u00fcler. Art\u0131klar grafik boyunca s\u0131f\u0131r de\u011feri etraf\u0131nda rastgele ve d\u00fczg\u00fcn bir \u015fekilde da\u011f\u0131lm\u0131\u015f g\u00f6r\u00fcnd\u00fc\u011f\u00fc s\u00fcrece, e\u015f varyansl\u0131l\u0131\u011f\u0131n ihlal edilmedi\u011fini varsayabiliriz:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define residuals\n<\/span>res &lt;- resid(model)\n\n<span style=\"color: #008080;\">#produce residual vs. fitted plot\n<\/span>plot(fitted(model), res)\n\n<span style=\"color: #008080;\">#add a horizontal line at 0 \n<\/span>abline(0,0)\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11533 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/simpleregr3.png\" alt=\"Basit do\u011frusal regresyon i\u00e7in R'de art\u0131k grafik\" width=\"382\" height=\"342\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Art\u0131klar s\u0131f\u0131r etraf\u0131nda rastgele da\u011f\u0131lm\u0131\u015f gibi g\u00f6r\u00fcn\u00fcyor ve fark edilebilir bir desen g\u00f6stermiyor, dolay\u0131s\u0131yla bu varsay\u0131m kar\u015f\u0131lan\u0131yor.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>QQ grafi\u011fi:<\/strong> Bu grafik, art\u0131klar\u0131n normal bir da\u011f\u0131l\u0131m takip edip etmedi\u011fini belirlemek i\u00e7in kullan\u0131\u015fl\u0131d\u0131r. \u00c7izimdeki veri de\u011ferleri 45 derecelik a\u00e7\u0131yla kabaca d\u00fcz bir \u00e7izgi izliyorsa veriler normal \u015fekilde da\u011f\u0131l\u0131r:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create QQ plot for residuals\n<\/span>qqnorm(res)\n\n<span style=\"color: #008080;\">#add a straight diagonal line to the plot\n<\/span>qqline(res) \n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11534 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/simpleregr4.png\" alt=\"R'de normal QQ grafi\u011fi\" width=\"385\" height=\"384\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Kal\u0131nt\u0131lar 45 derece \u00e7izgisinden biraz sap\u0131yor ancak ciddi endi\u015fe yaratacak kadar de\u011fil. Normallik varsay\u0131m\u0131n\u0131n kar\u015f\u0131land\u0131\u011f\u0131n\u0131 varsayabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Art\u0131klar normal da\u011f\u0131l\u0131ml\u0131 ve homoskedastik oldu\u011fundan, basit do\u011frusal regresyon modelinin varsay\u0131mlar\u0131n\u0131n kar\u015f\u0131land\u0131\u011f\u0131n\u0131 do\u011frulad\u0131k. Dolay\u0131s\u0131yla modelimizin \u00e7\u0131kt\u0131s\u0131 g\u00fcvenilirdir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>Bu e\u011fitimde kullan\u0131lan R kodunun tamam\u0131n\u0131 <a href=\"https:\/\/raw.githubusercontent.com\/Statorials\/R-Guides\/main\/simple_linear_regression.R\" target=\"_blank\" rel=\"noopener noreferrer\">burada<\/a> bulabilirsiniz.<\/em><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Basit do\u011frusal regresyon, tek bir a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fken ile tek bir yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkiyi anlamak i\u00e7in kullanabilece\u011fimiz bir tekniktir. \u00d6zetle, 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 : [&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-1151","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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