{"id":487,"date":"2023-07-29T18:10:23","date_gmt":"2023-07-29T18:10:23","guid":{"rendered":"https:\/\/statorials.org\/tr\/rdeki-veriler-nasil-normallestirilir\/"},"modified":"2023-07-29T18:10:23","modified_gmt":"2023-07-29T18:10:23","slug":"rdeki-veriler-nasil-normallestirilir","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/rdeki-veriler-nasil-normallestirilir\/","title":{"rendered":"R&#39;deki veriler nas\u0131l normalle\u015ftirilir"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u00c7o\u011fu durumda, insanlar bir veri k\u00fcmesindeki de\u011fi\u015fkenleri &#8220;normalle\u015ftirmekten&#8221; bahsettiklerinde, de\u011fi\u015fkenin ortalamas\u0131 0 ve standart sapmas\u0131 1 olacak \u015fekilde de\u011ferleri \u00f6l\u00e7eklendirmek istediklerini kastediyorlar.<\/span><\/p>\n<p> <span style=\"color: #000000;\">De\u011fi\u015fkenleri standartla\u015ft\u0131rman\u0131n en yayg\u0131n nedeni, bir t\u00fcr \u00e7ok de\u011fi\u015fkenli analiz ger\u00e7ekle\u015ftirmenizdir (yani, birden fazla yorday\u0131c\u0131 de\u011fi\u015fken ile bir yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkiyi anlamak istemeniz) ve her de\u011fi\u015fkenin analize e\u015fit \u015fekilde katk\u0131da bulunmas\u0131n\u0131 istemenizdir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">De\u011fi\u015fkenler farkl\u0131 \u00f6l\u00e7eklerde \u00f6l\u00e7\u00fcld\u00fc\u011f\u00fcnde \u00e7o\u011fu zaman analize e\u015fit katk\u0131 sa\u011flamazlar. \u00d6rne\u011fin bir de\u011fi\u015fkenin de\u011ferleri 0 ile 100.000 aras\u0131nda de\u011fi\u015fiyorsa ve ba\u015fka bir de\u011fi\u015fkenin de\u011ferleri 0 ile 100 aras\u0131nda de\u011fi\u015fiyorsa, aral\u0131\u011f\u0131 daha b\u00fcy\u00fck olan de\u011fi\u015fkene analizde daha fazla a\u011f\u0131rl\u0131k verilecektir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu, bir de\u011fi\u015fkenin maa\u015f gibi bir \u015feyi (0 ila 100.000 ABD Dolar\u0131) \u00f6l\u00e7t\u00fc\u011f\u00fc ve ba\u015fka bir de\u011fi\u015fkenin ya\u015f (0 ila 100 ya\u015f) gibi bir \u015feyi \u00f6l\u00e7t\u00fc\u011f\u00fc durumlarda yayg\u0131nd\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">De\u011fi\u015fkenleri standartla\u015ft\u0131rarak her de\u011fi\u015fkenin analize e\u015fit katk\u0131da bulundu\u011fundan emin olabiliriz. De\u011fi\u015fkenleri normalle\u015ftirmenin (veya &#8220;\u00f6l\u00e7eklendirmenin&#8221;) iki yayg\u0131n yolu vard\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Min-Maks normalizasyonu:<\/strong> (X \u2013 min(X)) \/ (max(X) \u2013 min(X))<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"color: #000000;\">Z puan\u0131n\u0131n standardizasyonu:<\/span><\/strong> (X \u2013 \u03bc) \/ \u03c3<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Daha sonra bu iki tekni\u011fin R&#8217;de nas\u0131l uygulanaca\u011f\u0131n\u0131 g\u00f6sterece\u011fiz.<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">R&#8217;de de\u011fi\u015fkenler nas\u0131l normalle\u015ftirilir (veya &#8220;\u00f6l\u00e7eklenir&#8221;)<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rneklerin her biri i\u00e7in, R&#8217;deki de\u011fi\u015fkenlerin nas\u0131l normalle\u015ftirilece\u011fini veya \u00f6l\u00e7eklendirilece\u011fini g\u00f6stermek i\u00e7in yerle\u015fik R veri k\u00fcmesi <strong>irisini<\/strong> kullanaca\u011f\u0131z:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <span style=\"color: #008080;\"><strong>#view first six rows of <em>iris<\/em> dataset\n<span style=\"color: #000000;\">head(iris)\n\n# Sepal.Length Sepal.Width Petal.Length Petal.Width Species\n#1 5.1 3.5 1.4 0.2 setosa\n#2 4.9 3.0 1.4 0.2 setosa\n#3 4.7 3.2 1.3 0.2 setosa\n#4 4.6 3.1 1.5 0.2 setosa\n#5 5.0 3.6 1.4 0.2 setosa\n#6 5.4 3.9 1.7 0.4 setosa\n<\/span><\/strong><\/span><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Min-Maks Normalle\u015ftirme<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Min-max normalizasyonunun form\u00fcl\u00fc \u015f\u00f6yledir:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">(X \u2013 min(X))\/(maks(X) \u2013 min(X))<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir de\u011fi\u015fkenin her de\u011feri i\u00e7in, o de\u011fer ile minimum de\u011fer aras\u0131ndaki mesafeyi bulup aral\u0131\u011fa b\u00f6leriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunu R&#8217;de uygulamak i\u00e7in basit bir fonksiyon tan\u0131mlayabilir ve ard\u0131ndan bu fonksiyonu istedi\u011fimiz <strong>iris<\/strong> veri k\u00fcmesindeki s\u00fctunlara uygulamak i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/rde-lapply-sapply-ve-tapply-uygulama-kilavuzu\/\" target=\"_blank\" rel=\"noopener\">laply&#8217;yi<\/a> kullanabiliriz:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define Min-Max normalization function<\/span>\nmin_max_norm &lt;- <span style=\"color: #800080;\">function<\/span> (x) {\n    (x - min(x)) \/ (max(x) - min(x))\n  }\n\n<span style=\"color: #008080;\">#apply Min-Max normalization to first four columns in <em>iris<\/em> dataset\n<span style=\"color: #000000;\">iris_norm &lt;- as.data.frame(lapply(iris[1:4], min_max_norm))\n\n<span style=\"color: #008080;\">#view first six rows of normalized <em>iris<\/em> dataset<\/span>\nhead(iris_norm)\n\n# Sepal.Length Sepal.Width Petal.Length Petal.Width\n#1 0.22222222 0.6250000 0.06779661 0.04166667\n#2 0.16666667 0.4166667 0.06779661 0.04166667\n#3 0.11111111 0.5000000 0.05084746 0.04166667\n#4 0.08333333 0.4583333 0.08474576 0.04166667\n#5 0.19444444 0.6666667 0.06779661 0.04166667\n#6 0.30555556 0.7916667 0.11864407 0.12500000\n<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">S\u00fctunlar\u0131n her birinin art\u0131k 0 ile 1 aras\u0131nda de\u011ferlere sahip oldu\u011funu unutmay\u0131n. Ayr\u0131ca be\u015finci s\u00fctun &#8220;T\u00fcrler&#8221;in bu veri \u00e7er\u00e7evesinden kald\u0131r\u0131ld\u0131\u011f\u0131n\u0131 da unutmay\u0131n. A\u015fa\u011f\u0131daki kodu kullanarak kolayca ekleyebiliriz:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#add back <em>Species<\/em> column<\/span>\niris_norm$Species &lt;- iris$Species\n\n<span style=\"color: #008080;\">#view first six rows of <em>iris_norm\n<\/em><\/span>head(iris_norm)\n\n# Sepal.Length Sepal.Width Petal.Length Petal.Width Species\n#1 0.22222222 0.6250000 0.06779661 0.04166667 setosa\n#2 0.16666667 0.4166667 0.06779661 0.04166667 setosa\n#3 0.11111111 0.5000000 0.05084746 0.04166667 setosa\n#4 0.08333333 0.4583333 0.08474576 0.04166667 setosa\n#5 0.19444444 0.6666667 0.06779661 0.04166667 setosa\n#6 0.30555556 0.7916667 0.11864407 0.12500000 setosa\n<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Z puan\u0131 standardizasyonu<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Min-max normalizasyon tekni\u011finin dezavantaj\u0131 veri de\u011ferlerini ortalamaya yakla\u015ft\u0131rmas\u0131d\u0131r. Ayk\u0131r\u0131 de\u011ferlerin di\u011fer de\u011ferlerden daha fazla a\u011f\u0131rl\u0131kland\u0131r\u0131lmas\u0131n\u0131 sa\u011flamak istiyorsak, z-puan\u0131 standardizasyonunun uygulanmas\u0131 daha iyi bir tekniktir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Z-puan\u0131n\u0131 standartla\u015ft\u0131rma form\u00fcl\u00fc a\u015fa\u011f\u0131daki gibidir:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">(X \u2013 \u03bc) \/ \u03c3<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir de\u011fi\u015fkenin her bir de\u011feri i\u00e7in, de\u011fi\u015fkenin ortalama de\u011ferini \u00e7\u0131kar\u0131r\u0131z ve ard\u0131ndan de\u011fi\u015fkenin standart sapmas\u0131na b\u00f6leriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunu R&#8217;de uygulamak i\u00e7in birka\u00e7 se\u00e7ene\u011fimiz var:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Bir de\u011fi\u015fkeni standartla\u015ft\u0131r\u0131n<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u0130ris<\/strong> veri k\u00fcmesindeki Sepal.Width gibi bir veri k\u00fcmesindeki bir de\u011fi\u015fkeni standartla\u015ft\u0131rmak istiyorsak a\u015fa\u011f\u0131daki kodu kullanabiliriz:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#standardize<\/span> <span style=\"color: #008080;\"><em>Sepal.Width\n<\/em><\/span>iris$Sepal.Width &lt;- (iris$Sepal.Width - mean(iris$Sepal.Width)) \/ sd(iris$Sepal.Width)\n\nhead(iris)\n\n# Sepal.Length Sepal.Width Petal.Length Petal.Width Species\n#1 5.1 1.01560199 1.4 0.2 setosa\n#2 4.9 -0.13153881 1.4 0.2 setosa\n#3 4.7 0.32731751 1.3 0.2 setosa\n#4 4.6 0.09788935 1.5 0.2 setosa\n#5 5.0 1.24503015 1.4 0.2 setosa\n#6 5.4 1.93331463 1.7 0.4 setosa\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><em>Sepal.Width<\/em> de\u011ferleri art\u0131k ortalama 0 ve standart sapma 1 olacak \u015fekilde \u00f6l\u00e7eklendirilmi\u015ftir. Hatta istersek bunu kontrol edebiliriz:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#find mean of <em>Sepal.Width\n<\/em><\/span>mean(iris$Sepal.Width)\n\n#[1] 2.034094e-16 <span style=\"color: #008080;\">#basically zero<\/span>\n\n<span style=\"color: #008080;\">#find standard deviation of <em>Sepal.Width\n<\/em><\/span>sd(iris$Sepal.Width)\n\n#[1] 1<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>2. \u00d6l\u00e7ek fonksiyonunu kullanarak birden fazla de\u011fi\u015fkeni standartla\u015ft\u0131r\u0131n<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Birden fazla de\u011fi\u015fkeni normalle\u015ftirmek i\u00e7in <em>\u00f6l\u00e7ek<\/em> fonksiyonu basit\u00e7e kullan\u0131labilir. \u00d6rne\u011fin, a\u015fa\u011f\u0131daki kod <strong>iris<\/strong> veri k\u00fcmesinin ilk d\u00f6rt s\u00fctununun nas\u0131l \u00f6l\u00e7eklendirilece\u011fini g\u00f6sterir:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#standardize first four columns of <em>iris<\/em> dataset<\/span>\niris_standardize &lt;- as.data.frame(scale(iris[1:4]))\n\n<span style=\"color: #008080;\">#view first six rows of standardized dataset<\/span>\n<\/strong><\/span><strong>head(iris_standardize)\n\n# Sepal.Length Sepal.Width Petal.Length Petal.Width\n#1 -0.8976739 1.01560199 -1.335752 -1.311052\n#2 -1.1392005 -0.13153881 -1.335752 -1.311052\n#3 -1.3807271 0.32731751 -1.392399 -1.311052\n#4 -1.5014904 0.09788935 -1.279104 -1.311052\n#5 -1.0184372 1.24503015 -1.335752 -1.311052\n#6 -0.5353840 1.93331463 -1.165809 -1.048667\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><em>\u00d6l\u00e7ek<\/em> fonksiyonunun varsay\u0131lan olarak bir veri \u00e7er\u00e7evesindeki her s\u00fctunu normalle\u015ftirmeye \u00e7al\u0131\u015ft\u0131\u011f\u0131n\u0131 unutmay\u0131n. Dolay\u0131s\u0131yla, <em>T\u00fcrler<\/em> s\u00fctunu say\u0131sal olmad\u0131\u011f\u0131 ve standartla\u015ft\u0131r\u0131lamad\u0131\u011f\u0131 i\u00e7in <strong>\u00f6l\u00e7ek(iris)<\/strong> kullanmay\u0131 denedi\u011fimizde bir hata al\u0131r\u0131z:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong>scale(iris)\n\n#Error in colMeans(x, na.rm = TRUE): 'x' must be numeric\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Ancak <strong>dplyr<\/strong> paketini kullanarak bir veri \u00e7er\u00e7evesindeki yaln\u0131zca belirli de\u011fi\u015fkenleri standartla\u015ft\u0131r\u0131rken di\u011fer t\u00fcm de\u011fi\u015fkenleri ayn\u0131 tutmak m\u00fcmk\u00fcnd\u00fcr. \u00d6rne\u011fin, a\u015fa\u011f\u0131daki kod <em>Sepal.Width<\/em> ve <em>Sepal.Length<\/em> de\u011fi\u015fkenlerini standartla\u015ft\u0131r\u0131rken di\u011fer t\u00fcm de\u011fi\u015fkenleri ayn\u0131 tutar:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load <em>dplyr<\/em> package<\/span>\nlibrary(dplyr)\n\n<span style=\"color: #008080;\">#standardize <em>Sepal.Width<\/em> and <em>Sepal.Length<\/em>\n<\/span>iris_new &lt;- iris %&gt;% mutate_each_(list(~scale(.) %&gt;% as.vector),\n                                  vars = c(\"Sepal.Width\",\"Sepal.Length\"))\n\n<span style=\"color: #008080;\">#view first six rows of new data frame\n<\/span>head(iris_new)\n\n# Sepal.Length Sepal.Width Petal.Length Petal.Width Species\n#1 -0.8976739 1.01560199 1.4 0.2 setosa\n#2 -1.1392005 -0.13153881 1.4 0.2 setosa\n#3 -1.3807271 0.32731751 1.3 0.2 setosa\n#4 -1.5014904 0.09788935 1.5 0.2 setosa\n#5 -1.0184372 1.24503015 1.4 0.2 setosa\n#6 -0.5353840 1.93331463 1.7 0.4 setosa\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><em>Sepal.Length<\/em> ve <em>Sepal.Width&#8217;in<\/em> , her iki de\u011fi\u015fkenin de ortalamas\u0131 0 ve standart sapmas\u0131 1 olacak \u015fekilde standartla\u015ft\u0131r\u0131ld\u0131\u011f\u0131n\u0131, veri \u00e7er\u00e7evesindeki di\u011fer \u00fc\u00e7 de\u011fi\u015fkenin ise de\u011fi\u015fmedi\u011fini unutmay\u0131n.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00c7o\u011fu durumda, insanlar bir veri k\u00fcmesindeki de\u011fi\u015fkenleri &#8220;normalle\u015ftirmekten&#8221; bahsettiklerinde, de\u011fi\u015fkenin ortalamas\u0131 0 ve standart sapmas\u0131 1 olacak \u015fekilde de\u011ferleri \u00f6l\u00e7eklendirmek istediklerini kastediyorlar. De\u011fi\u015fkenleri standartla\u015ft\u0131rman\u0131n en yayg\u0131n nedeni, bir t\u00fcr \u00e7ok de\u011fi\u015fkenli analiz ger\u00e7ekle\u015ftirmenizdir (yani, birden fazla yorday\u0131c\u0131 de\u011fi\u015fken ile bir yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkiyi anlamak istemeniz) ve her de\u011fi\u015fkenin analize e\u015fit \u015fekilde katk\u0131da bulunmas\u0131n\u0131 istemenizdir. [&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-487","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 - Statorials&#039;ta veriler nas\u0131l normalle\u015ftirilir?<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde R&#039;deki verileri kolayca normalle\u015ftirmenin veya \u00f6l\u00e7eklendirmenin \u00e7e\u015fitli yollar\u0131 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\/rdeki-veriler-nasil-normallestirilir\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"R - Statorials&#039;ta veriler nas\u0131l normalle\u015ftirilir?\" \/>\n<meta property=\"og:description\" content=\"Bu e\u011fitimde R&#039;deki verileri kolayca normalle\u015ftirmenin veya \u00f6l\u00e7eklendirmenin \u00e7e\u015fitli yollar\u0131 a\u00e7\u0131klanmaktad\u0131r.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/rdeki-veriler-nasil-normallestirilir\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-29T18:10:23+00:00\" \/>\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=\"5 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/rdeki-veriler-nasil-normallestirilir\/\",\"url\":\"https:\/\/statorials.org\/tr\/rdeki-veriler-nasil-normallestirilir\/\",\"name\":\"R - Statorials&#39;ta veriler nas\u0131l normalle\u015ftirilir?\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-29T18:10:23+00:00\",\"dateModified\":\"2023-07-29T18:10:23+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Bu e\u011fitimde R&#39;deki verileri kolayca normalle\u015ftirmenin veya \u00f6l\u00e7eklendirmenin \u00e7e\u015fitli yollar\u0131 a\u00e7\u0131klanmaktad\u0131r.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/rdeki-veriler-nasil-normallestirilir\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/rdeki-veriler-nasil-normallestirilir\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/rdeki-veriler-nasil-normallestirilir\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"R&#39;deki veriler nas\u0131l normalle\u015ftirilir\"}]},{\"@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. 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