{"id":1210,"date":"2023-07-27T06:58:14","date_gmt":"2023-07-27T06:58:14","guid":{"rendered":"https:\/\/statorials.org\/tr\/rde-kismi-en-kucuk-kareler\/"},"modified":"2023-07-27T06:58:14","modified_gmt":"2023-07-27T06:58:14","slug":"rde-kismi-en-kucuk-kareler","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/rde-kismi-en-kucuk-kareler\/","title":{"rendered":"R&#39;de k\u0131smi en k\u00fc\u00e7\u00fck kareler (ad\u0131m ad\u0131m)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Makine \u00f6\u011freniminde kar\u015f\u0131la\u015faca\u011f\u0131n\u0131z en yayg\u0131n sorunlardan biri <a href=\"https:\/\/statorials.org\/tr\/coklu-baglanti-regresyonu\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u00e7oklu ba\u011flant\u0131d\u0131r<\/a> . Bu, bir veri setindeki iki veya daha fazla \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkenin y\u00fcksek d\u00fczeyde korelasyona sahip olmas\u0131 durumunda ortaya \u00e7\u0131kar.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu oldu\u011funda, bir model bir e\u011fitim veri setine iyi uyum sa\u011flayabilir, ancak e\u011fitim veri setine <a href=\"https:\/\/statorials.org\/tr\/makine-ogrenimi-asiri-uyumu\/\" target=\"_blank\" rel=\"noopener noreferrer\">fazla uyum<\/a> sa\u011flad\u0131\u011f\u0131 i\u00e7in daha \u00f6nce g\u00f6rmedi\u011fi yeni bir veri setinde d\u00fc\u015f\u00fck performans g\u00f6sterebilir. E\u011fitim Seti.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu sorunu a\u015fman\u0131n bir yolu <a href=\"https:\/\/statorials.org\/tr\/kismi-en-kucuk-kareler\/\" target=\"_blank\" rel=\"noopener noreferrer\">, k\u0131smi en k\u00fc\u00e7\u00fck kareler<\/a> ad\u0131 verilen ve \u015fu \u015fekilde \u00e7al\u0131\u015fan bir y\u00f6ntem kullanmakt\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Tahmin edici ve yan\u0131t de\u011fi\u015fkenlerini standartla\u015ft\u0131r\u0131n.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Hem yan\u0131t de\u011fi\u015fkenindeki hem de yorday\u0131c\u0131 de\u011fi\u015fkenlerdeki \u00f6nemli miktarda varyasyonu a\u00e7\u0131klayan<\/span> <em style=\"color: #000000;\">p<\/em> orijinal yorday\u0131c\u0131 <span style=\"color: #000000;\">de\u011fi\u015fkenin <em>M<\/em> do\u011frusal kombinasyonunu (&#8220;PLS bile\u015fenleri&#8221; olarak adland\u0131r\u0131l\u0131r) hesaplay\u0131n<\/span> .<\/li>\n<li> <span style=\"color: #000000;\">Tahmin edici olarak PLS bile\u015fenlerini kullanarak do\u011frusal bir regresyon modeline uymak i\u00e7in en k\u00fc\u00e7\u00fck kareler y\u00f6ntemini kullan\u0131n.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Modelde tutulacak en uygun PLS bile\u015feni say\u0131s\u0131n\u0131 bulmak i\u00e7in<\/span> <a href=\"https:\/\/statorials.org\/tr\/k-kat-capraz-dogrulama\/\" target=\"_blank\" rel=\"noopener noreferrer\">k-katl\u0131 \u00e7apraz do\u011frulamay\u0131<\/a> <span style=\"color: #000000;\">kullan\u0131n<\/span> .<\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu e\u011fitimde, R&#8217;de k\u0131smi en k\u00fc\u00e7\u00fck karelerin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fine ili\u015fkin ad\u0131m ad\u0131m bir \u00f6rnek sunulmaktad\u0131r.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ad\u0131m 1: Gerekli paketleri y\u00fckleyin<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">R&#8217;de k\u0131smi en k\u00fc\u00e7\u00fck kareler ger\u00e7ekle\u015ftirmenin en kolay yolu <a href=\"https:\/\/cran.r-project.org\/web\/packages\/pls\/pls.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">pls<\/a> paketindeki i\u015flevleri kullanmakt\u0131r.<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#install pls package (if not already installed)<\/span>\ninstall.packages(\" <span style=\"color: #008000;\">pls<\/span> \")\n\n<span style=\"color: #008080;\">load pls package\n<\/span>library(pls)\n<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Ad\u0131m 2: K\u0131smi en k\u00fc\u00e7\u00fck kareler modelini yerle\u015ftirin<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnek i\u00e7in, farkl\u0131 araba t\u00fcrlerine ili\u015fkin verileri i\u00e7eren <strong>mtcars<\/strong> ad\u0131 verilen yerle\u015fik R veri k\u00fcmesini kullanaca\u011f\u0131z:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#view first six rows of mtcars dataset<\/span>\nhead(mtcars)\n\n                   mpg cyl disp hp drat wt qsec vs am gear carb\nMazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4\nMazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4\nDatsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1\nHornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1\nHornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2\nValiant 18.1 6 225 105 2.76 3,460 20.22 1 0 3 1\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnek i\u00e7in, <a href=\"https:\/\/statorials.org\/tr\/degiskenleri-aciklayici-yanitlar\/\" target=\"_blank\" rel=\"noopener noreferrer\">yan\u0131t<\/a> de\u011fi\u015fkeni olarak <em>hp&#8217;yi<\/em> ve tahmin de\u011fi\u015fkenleri olarak a\u015fa\u011f\u0131daki de\u011fi\u015fkenleri kullanarak k\u0131smi en k\u00fc\u00e7\u00fck kareler (PLS) modelini uygulayaca\u011f\u0131z:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">mpg<\/span><\/li>\n<li> <span style=\"color: #000000;\">g\u00f6r\u00fcnt\u00fclemek<\/span><\/li>\n<li> <span style=\"color: #000000;\">bok<\/span><\/li>\n<li> <span style=\"color: #000000;\">a\u011f\u0131rl\u0131k<\/span><\/li>\n<li> <span style=\"color: #000000;\">qsec<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, PLS modelinin bu verilere nas\u0131l s\u0131\u011fd\u0131r\u0131laca\u011f\u0131n\u0131 g\u00f6sterir. A\u015fa\u011f\u0131daki arg\u00fcmanlara dikkat edin:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u00f6l\u00e7ek=DO\u011eRU<\/strong> : Bu, R&#8217;ye, veri k\u00fcmesindeki de\u011fi\u015fkenlerin her birinin ortalamas\u0131 0 ve standart sapmas\u0131 1 olacak \u015fekilde \u00f6l\u00e7eklendirilmesi gerekti\u011fini s\u00f6yler. Bu, farkl\u0131 birimlerle \u00f6l\u00e7\u00fcld\u00fc\u011f\u00fcnde hi\u00e7bir yorday\u0131c\u0131 de\u011fi\u015fkenin modelde \u00e7ok fazla etkiye sahip olmamas\u0131n\u0131 sa\u011flar.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>validation=\u201dCV\u201d<\/strong> : Bu, R&#8217;ye model performans\u0131n\u0131 de\u011ferlendirmek i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/k-kat-capraz-dogrulama\/\" target=\"_blank\" rel=\"noopener noreferrer\">k-katl\u0131 \u00e7apraz do\u011frulama<\/a> kullanmas\u0131n\u0131 s\u00f6yler. Bunun varsay\u0131lan olarak k=10 kat kulland\u0131\u011f\u0131n\u0131 unutmay\u0131n. Ayr\u0131ca <a href=\"https:\/\/statorials.org\/tr\/tek-bir-capraz-dogrulama-birakin\/\" target=\"_blank\" rel=\"noopener noreferrer\">Birini D\u0131\u015far\u0131da B\u0131rakma \u00e7apraz do\u011frulamas\u0131<\/a> ger\u00e7ekle\u015ftirmek yerine &#8220;LOOCV&#8221;yi belirtebilece\u011finizi de unutmay\u0131n.<\/span><\/li>\n<\/ul>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#make this example reproducible\n<\/span>set.seed(1)\n\n<span style=\"color: #008080;\">#fit PCR model\n<\/span>model &lt;- plsr(hp~mpg+disp+drat+wt+qsec, data=mtcars, scale= <span style=\"color: #008000;\">TRUE<\/span> , validation=\" <span style=\"color: #008000;\">CV<\/span> \")<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Ad\u0131m 3: PLS bile\u015fenlerinin say\u0131s\u0131n\u0131 se\u00e7in<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Modeli yerle\u015ftirdikten sonra ka\u00e7 tane PLS bile\u015feni tutaca\u011f\u0131m\u0131z\u0131 belirlememiz gerekiyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunu yapmak i\u00e7in k-\u00e7apraz do\u011frulamayla hesaplanan test k\u00f6k ortalama kare hatas\u0131na (test RMSE) bakman\u0131z yeterlidir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#view summary of model fitting\n<\/span>summary(model)\n\nData: \n\tY dimension: 32 1\nFit method: kernelpls\nNumber of components considered: 5\n\nVALIDATION: RMSEP\nCross-validated using 10 random segments.\n       (Intercept) 1 comp 2 comps 3 comps 4 comps 5 comps\nCV 69.66 40.57 35.48 36.22 36.74 36.67\nadjCV 69.66 40.41 35.12 35.80 36.27 36.20\n\nTRAINING: % variance explained\n    1 comp 2 comps 3 comps 4 comps 5 comps\nX 68.66 89.27 95.82 97.94 100.00\nhp 71.84 81.74 82.00 82.02 82.03\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Sonu\u00e7ta iki ilgin\u00e7 tablo var:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. DO\u011eRULAMA: RMSEP<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu tablo bize k-katl\u0131 \u00e7apraz do\u011frulamayla hesaplanan RMSE testini anlat\u0131r. A\u015fa\u011f\u0131dakileri g\u00f6rebiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Modelde sadece orijinal terimi kullan\u0131rsak testin RMSE&#8217;si <strong>69,66<\/strong> olur.<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0130lk PLS bile\u015fenini de eklersek RMSE testi <strong>40,57&#8217;ye d\u00fc\u015f\u00fcyor.<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0130kinci PLS bile\u015fenini de eklersek RMSE testi <strong>35,48&#8217;e d\u00fc\u015f\u00fcyor.<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Ek PLS bile\u015fenlerinin eklenmesinin asl\u0131nda testin RMSE&#8217;sinde art\u0131\u015fa yol a\u00e7t\u0131\u011f\u0131n\u0131 g\u00f6rebiliriz. Dolay\u0131s\u0131yla nihai modelde yaln\u0131zca iki PLS bile\u015feninin kullan\u0131lmas\u0131n\u0131n optimal olaca\u011f\u0131 g\u00f6r\u00fclmektedir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. E\u011e\u0130T\u0130M: a\u00e7\u0131klanan varyans y\u00fczdesi<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu tablo bize PLS bile\u015fenleri taraf\u0131ndan a\u00e7\u0131klanan yan\u0131t de\u011fi\u015fkenindeki varyans\u0131n y\u00fczdesini g\u00f6sterir. A\u015fa\u011f\u0131dakileri g\u00f6rebiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Yaln\u0131zca ilk PLS bile\u015fenini kullanarak yan\u0131t de\u011fi\u015fkenindeki varyasyonun <strong>%68,66&#8217;s\u0131n\u0131<\/strong> a\u00e7\u0131klayabiliriz.<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0130kinci PLS bile\u015fenini ekleyerek yan\u0131t de\u011fi\u015fkenindeki varyasyonun <strong>%89,27&#8217;sini<\/strong> a\u00e7\u0131klayabiliriz.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Daha fazla PLS bile\u015feni kullanarak hala daha fazla varyans\u0131 a\u00e7\u0131klayabilece\u011fimizi unutmay\u0131n, ancak ikiden fazla PLS bile\u015feni eklemenin asl\u0131nda a\u00e7\u0131klanan varyans y\u00fczdesini \u00e7ok fazla art\u0131rmad\u0131\u011f\u0131n\u0131 g\u00f6rebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Validationplot()<\/strong> i\u015flevini kullanarak RMSE testini (MSE ve R-kare testiyle birlikte) PLS bile\u015fenlerinin say\u0131s\u0131n\u0131n bir fonksiyonu olarak da g\u00f6rselle\u015ftirebiliriz.<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#visualize cross-validation plots\n<\/span>validationplot(model)\nvalidationplot(model, val.type=\" <span style=\"color: #008000;\">MSEP<\/span> \")\nvalidationplot(model, val.type=\" <span style=\"color: #008000;\">R2<\/span> \")<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11975 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/svpr1.png\" alt=\"R'de k\u0131smi en k\u00fc\u00e7\u00fck kareler\" width=\"396\" height=\"382\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11976 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/sil-vous-plaitr2.png\" alt=\"R'de MSE \u00e7apraz do\u011frulama\" width=\"396\" height=\"391\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11977 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/sil-vous-plaitr3.png\" alt=\"R'deki k\u0131smi en k\u00fc\u00e7\u00fck kareler i\u00e7in \u00e7apraz do\u011frulama\" width=\"397\" height=\"387\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Her grafikte, iki PLS bile\u015feni eklendi\u011finde model uyumunun artt\u0131\u011f\u0131n\u0131 ancak daha fazla PLS bile\u015feni ekledi\u011fimizde bozulma e\u011filiminde oldu\u011funu g\u00f6rebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu nedenle optimal model yaln\u0131zca ilk iki PLS bile\u015fenini i\u00e7erir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ad\u0131m 4: Tahminlerde bulunmak i\u00e7in son modeli kullan\u0131n<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Yeni g\u00f6zlemler hakk\u0131nda tahminlerde bulunmak i\u00e7in son modeli iki PLS bile\u015feniyle kullanabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, orijinal veri k\u00fcmesinin bir e\u011fitim ve test k\u00fcmesine nas\u0131l b\u00f6l\u00fcnece\u011fini ve test k\u00fcmesi \u00fczerinde tahminler yapmak i\u00e7in iki PLS bile\u015feniyle son modelin nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define training and testing sets\n<\/span>train &lt;- mtcars[1:25, c(\"hp\", \"mpg\", \"disp\", \"drat\", \"wt\", \"qsec\")]\ny_test &lt;- mtcars[26: <span style=\"color: #3366ff;\">nrow<\/span> (mtcars), c(\"hp\")]\ntest &lt;- mtcars[26: <span style=\"color: #3366ff;\">nrow<\/span> (mtcars), c(\"mpg\", \"disp\", \"drat\", \"wt\", \"qsec\")]\n    \n<span style=\"color: #008080;\">#use model to make predictions on a test set\n<\/span>model &lt;- plsr(hp~mpg+disp+drat+wt+qsec, data=train, scale= <span style=\"color: #008000;\">TRUE<\/span> , validation=\" <span style=\"color: #008000;\">CV<\/span> \")\npcr_pred &lt;- predict(model, test, ncomp= <span style=\"color: #008000;\">2<\/span> )\n\n<span style=\"color: #008080;\">#calculate RMSE\n<\/span><span style=\"color: #3366ff;\">sqrt<\/span> ( <span style=\"color: #3366ff;\">mean<\/span> ((pcr_pred - y_test)^2))\n\n[1] 54.89609\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Testin RMSE&#8217;sinin <strong>54,89609<\/strong> oldu\u011funu g\u00f6r\u00fcyoruz. Bu, test seti g\u00f6zlemleri i\u00e7in tahmin edilen <em>hp<\/em> de\u011feri ile g\u00f6zlenen <em>hp<\/em> de\u011feri aras\u0131ndaki ortalama sapmad\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130ki temel bile\u015fene sahip <a href=\"https:\/\/statorials.org\/tr\/rde-temel-bilesenler-regresyonu\/\" target=\"_blank\" rel=\"noopener noreferrer\">e\u015fde\u011fer bir temel bile\u015fenler regresyon modelinin<\/a> <strong>56,86549<\/strong> de\u011ferinde bir test RMSE&#8217;si \u00fcretti\u011fini unutmay\u0131n. Dolay\u0131s\u0131yla PLS modeli bu veri seti i\u00e7in PCR modelinden biraz daha iyi performans g\u00f6sterdi.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekteki R kodunun tam kullan\u0131m\u0131n\u0131 <a href=\"https:\/\/github.com\/Statorials\/R-Guides\/blob\/main\/partial_least_squares.R\" target=\"_blank\" rel=\"noopener noreferrer\">burada<\/a> bulabilirsiniz.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Makine \u00f6\u011freniminde kar\u015f\u0131la\u015faca\u011f\u0131n\u0131z en yayg\u0131n sorunlardan biri \u00e7oklu ba\u011flant\u0131d\u0131r . Bu, bir veri setindeki iki veya daha fazla \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkenin y\u00fcksek d\u00fczeyde korelasyona sahip olmas\u0131 durumunda ortaya \u00e7\u0131kar. Bu oldu\u011funda, bir model bir e\u011fitim veri setine iyi uyum sa\u011flayabilir, ancak e\u011fitim veri setine fazla uyum sa\u011flad\u0131\u011f\u0131 i\u00e7in daha \u00f6nce g\u00f6rmedi\u011fi yeni bir veri setinde d\u00fc\u015f\u00fck [&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-1210","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>R&#039;de K\u0131smi En K\u00fc\u00e7\u00fck Kareler (ad\u0131m ad\u0131m)<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, ad\u0131m ad\u0131m bir \u00f6rnek de dahil olmak \u00fczere R&#039;de k\u0131smi en k\u00fc\u00e7\u00fck karelerin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi 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\/rde-kismi-en-kucuk-kareler\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"R&#039;de K\u0131smi En K\u00fc\u00e7\u00fck Kareler (ad\u0131m ad\u0131m)\" \/>\n<meta property=\"og:description\" content=\"Bu e\u011fitimde, ad\u0131m ad\u0131m bir \u00f6rnek de dahil olmak \u00fczere R&#039;de k\u0131smi en k\u00fc\u00e7\u00fck karelerin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/rde-kismi-en-kucuk-kareler\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-27T06:58:14+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/svpr1.png\" \/>\n<meta name=\"author\" content=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/rde-kismi-en-kucuk-kareler\/\",\"url\":\"https:\/\/statorials.org\/tr\/rde-kismi-en-kucuk-kareler\/\",\"name\":\"R&#39;de K\u0131smi En K\u00fc\u00e7\u00fck Kareler (ad\u0131m ad\u0131m)\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-27T06:58:14+00:00\",\"dateModified\":\"2023-07-27T06:58:14+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Bu e\u011fitimde, ad\u0131m ad\u0131m bir \u00f6rnek de dahil olmak \u00fczere R&#39;de k\u0131smi en k\u00fc\u00e7\u00fck karelerin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/rde-kismi-en-kucuk-kareler\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/rde-kismi-en-kucuk-kareler\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/rde-kismi-en-kucuk-kareler\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"R&#39;de k\u0131smi en k\u00fc\u00e7\u00fck kareler (ad\u0131m ad\u0131m)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/tr\/#website\",\"url\":\"https:\/\/statorials.org\/tr\/\",\"name\":\"Statorials\",\"description\":\"\u0130statistik okuryazarl\u0131\u011f\u0131 rehberiniz!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/tr\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"tr\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\",\"name\":\"Dr.benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"tr\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr.benjamin anderson\"},\"description\":\"Merhaba, ben Benjamin, emekli bir istatistik profes\u00f6r\u00fc ve Statorials \u00f6\u011fretmenine d\u00f6n\u00fc\u015ft\u00fcm. \u0130statistik alan\u0131ndaki kapsaml\u0131 deneyimim ve uzmanl\u0131\u011f\u0131mla, \u00f6\u011frencilerimi Statorials arac\u0131l\u0131\u011f\u0131yla g\u00fc\u00e7lendirmek i\u00e7in bilgilerimi payla\u015fmaya can at\u0131yorum. Daha fazlas\u0131n\u0131 bil\",\"sameAs\":[\"https:\/\/statorials.org\/tr\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"R&#39;de K\u0131smi En K\u00fc\u00e7\u00fck Kareler (ad\u0131m ad\u0131m)","description":"Bu e\u011fitimde, ad\u0131m ad\u0131m bir \u00f6rnek de dahil olmak \u00fczere R&#39;de k\u0131smi en k\u00fc\u00e7\u00fck karelerin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/statorials.org\/tr\/rde-kismi-en-kucuk-kareler\/","og_locale":"tr_TR","og_type":"article","og_title":"R&#39;de K\u0131smi En K\u00fc\u00e7\u00fck Kareler (ad\u0131m ad\u0131m)","og_description":"Bu e\u011fitimde, ad\u0131m ad\u0131m bir \u00f6rnek de dahil olmak \u00fczere R&#39;de k\u0131smi en k\u00fc\u00e7\u00fck karelerin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r.","og_url":"https:\/\/statorials.org\/tr\/rde-kismi-en-kucuk-kareler\/","og_site_name":"Statorials","article_published_time":"2023-07-27T06:58:14+00:00","og_image":[{"url":"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/svpr1.png"}],"author":"Dr.benjamin anderson","twitter_card":"summary_large_image","twitter_misc":{"Yazan:":"Dr.benjamin anderson","Tahmini okuma s\u00fcresi":"6 dakika"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/statorials.org\/tr\/rde-kismi-en-kucuk-kareler\/","url":"https:\/\/statorials.org\/tr\/rde-kismi-en-kucuk-kareler\/","name":"R&#39;de K\u0131smi En K\u00fc\u00e7\u00fck Kareler (ad\u0131m ad\u0131m)","isPartOf":{"@id":"https:\/\/statorials.org\/tr\/#website"},"datePublished":"2023-07-27T06:58:14+00:00","dateModified":"2023-07-27T06:58:14+00:00","author":{"@id":"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48"},"description":"Bu e\u011fitimde, ad\u0131m ad\u0131m bir \u00f6rnek de dahil olmak \u00fczere R&#39;de k\u0131smi en k\u00fc\u00e7\u00fck karelerin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r.","breadcrumb":{"@id":"https:\/\/statorials.org\/tr\/rde-kismi-en-kucuk-kareler\/#breadcrumb"},"inLanguage":"tr","potentialAction":[{"@type":"ReadAction","target":["https:\/\/statorials.org\/tr\/rde-kismi-en-kucuk-kareler\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/statorials.org\/tr\/rde-kismi-en-kucuk-kareler\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Ev","item":"https:\/\/statorials.org\/tr\/"},{"@type":"ListItem","position":2,"name":"R&#39;de k\u0131smi en k\u00fc\u00e7\u00fck kareler (ad\u0131m ad\u0131m)"}]},{"@type":"WebSite","@id":"https:\/\/statorials.org\/tr\/#website","url":"https:\/\/statorials.org\/tr\/","name":"Statorials","description":"\u0130statistik okuryazarl\u0131\u011f\u0131 rehberiniz!","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/statorials.org\/tr\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"tr"},{"@type":"Person","@id":"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48","name":"Dr.benjamin anderson","image":{"@type":"ImageObject","inLanguage":"tr","@id":"https:\/\/statorials.org\/tr\/#\/schema\/person\/image\/","url":"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg","contentUrl":"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg","caption":"Dr.benjamin anderson"},"description":"Merhaba, ben Benjamin, emekli bir istatistik profes\u00f6r\u00fc ve Statorials \u00f6\u011fretmenine d\u00f6n\u00fc\u015ft\u00fcm. \u0130statistik alan\u0131ndaki kapsaml\u0131 deneyimim ve uzmanl\u0131\u011f\u0131mla, \u00f6\u011frencilerimi Statorials arac\u0131l\u0131\u011f\u0131yla g\u00fc\u00e7lendirmek i\u00e7in bilgilerimi payla\u015fmaya can at\u0131yorum. Daha fazlas\u0131n\u0131 bil","sameAs":["https:\/\/statorials.org\/tr"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/posts\/1210","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/comments?post=1210"}],"version-history":[{"count":0,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/posts\/1210\/revisions"}],"wp:attachment":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/media?parent=1210"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/categories?post=1210"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/tags?post=1210"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}