{"id":3560,"date":"2023-07-16T20:16:40","date_gmt":"2023-07-16T20:16:40","guid":{"rendered":"https:\/\/statorials.org\/tr\/ols-regresyon-pitonu\/"},"modified":"2023-07-16T20:16:40","modified_gmt":"2023-07-16T20:16:40","slug":"ols-regresyon-pitonu","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ols-regresyon-pitonu\/","title":{"rendered":"Python&#39;da ols regresyon nas\u0131l ger\u00e7ekle\u015ftirilir (\u00f6rnekle)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">S\u0131radan en k\u00fc\u00e7\u00fck kareler (OLS) regresyonu, 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 en iyi tan\u0131mlayan do\u011fruyu bulmam\u0131z\u0131 sa\u011flayan bir y\u00f6ntemdir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu y\u00f6ntem a\u015fa\u011f\u0131daki denklemi bulmam\u0131z\u0131 sa\u011flar:<\/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, yorday\u0131c\u0131 ile yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkiyi anlamam\u0131za yard\u0131mc\u0131 olabilir ve yorday\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;\">A\u015fa\u011f\u0131daki ad\u0131m ad\u0131m \u00f6rnek, Python&#8217;da OLS regresyonunun nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini g\u00f6sterir.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><b>1. Ad\u0131m: Verileri olu\u015fturun<\/b><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte 15 \u00f6\u011frenci i\u00e7in a\u015fa\u011f\u0131daki iki de\u011fi\u015fkeni i\u00e7eren bir veri seti olu\u015fturaca\u011f\u0131z:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Toplam \u00e7al\u0131\u015f\u0131lan 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;\">Tahmin edici de\u011fi\u015fken olarak saatleri ve yan\u0131t de\u011fi\u015fkeni olarak s\u0131nav puan\u0131n\u0131 kullanarak bir OLS regresyonu ger\u00e7ekle\u015ftirece\u011fiz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, bu sahte veri k\u00fcmesinin pandalarda nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">import<\/span> pandas <span style=\"color: #008000;\">as<\/span> pd\n<span style=\"color: #008080;\">\n#createDataFrame<\/span>\ndf = pd. <span style=\"color: #3366ff;\">DataFrame<\/span> ({' <span style=\"color: #ff0000;\">hours<\/span> ': [1, 2, 4, 5, 5, 6, 6, 7, 8, 10, 11, 11, 12, 12, 14],\n                   ' <span style=\"color: #ff0000;\">score<\/span> ': [64, 66, 76, 73, 74, 81, 83, 82, 80, 88, 84, 82, 91, 93, 89]})\n\n<span style=\"color: #008080;\">#view DataFrame\n<\/span><span style=\"color: #008000;\">print<\/span> (df)\n\n    hours score\n0 1 64\n1 2 66\n2 4 76\n3 5 73\n4 5 74\n5 6 81\n6 6 83\n7 7 82\n8 8 80\n9 10 88\n10 11 84\n11 11 82\n12 12 91\n13 12 93\n14 14 89<\/strong><\/pre>\n<h2> <span style=\"color: #000000;\"><b>2. Ad\u0131m: Bir OLS regresyonu ger\u00e7ekle\u015ftirin<\/b><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Daha sonra, tahmin de\u011fi\u015fkeni olarak <strong>saatleri<\/strong> ve <strong>yan\u0131t<\/strong> de\u011fi\u015fkeni olarak puan\u0131 kullanarak bir OLS regresyonu ger\u00e7ekle\u015ftirmek i\u00e7in <a href=\"https:\/\/www.statsmodels.org\/stable\/index.html\" target=\"_blank\" rel=\"noopener\">statsmodels<\/a> mod\u00fcl\u00fcndeki i\u015flevleri kullanabiliriz:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008000;\">import<\/span> statsmodels.api <span style=\"color: #008000;\">as<\/span> sm\n<\/span>\n#define predictor and response variables\n<span style=\"color: #000000;\">y = df[' <span style=\"color: #ff0000;\">score<\/span> ']\nx = df[' <span style=\"color: #ff0000;\">hours<\/span> ']<\/span>\n\n#add constant to predictor variables\n<span style=\"color: #000000;\">x = sm. <span style=\"color: #3366ff;\">add_constant<\/span> (x)\n<\/span>\n#fit linear regression model\n<span style=\"color: #000000;\">model = sm. <span style=\"color: #3366ff;\">OLS<\/span> (y,x). <span style=\"color: #3366ff;\">fit<\/span> ()\n<\/span>\n#view model summary\n<span style=\"color: #000000;\"><span style=\"color: #008000;\">print<\/span> ( <span style=\"color: #3366ff;\">model.summary<\/span> ())\n\n                            OLS Regression Results                            \n==================================================== ============================\nDept. Variable: R-squared score: 0.831\nModel: OLS Adj. R-squared: 0.818\nMethod: Least Squares F-statistic: 63.91\nDate: Fri, 26 Aug 2022 Prob (F-statistic): 2.25e-06\nTime: 10:42:24 Log-Likelihood: -39,594\nNo. Observations: 15 AIC: 83.19\nDf Residuals: 13 BIC: 84.60\nModel: 1                                         \nCovariance Type: non-robust                                         \n==================================================== ============================\n                 coef std err t P&gt;|t| [0.025 0.975]\n-------------------------------------------------- ----------------------------\nconst 65.3340 2.106 31.023 0.000 60.784 69.884\nhours 1.9824 0.248 7.995 0.000 1.447 2.518\n==================================================== ============================\nOmnibus: 4,351 Durbin-Watson: 1,677\nProb(Omnibus): 0.114 Jarque-Bera (JB): 1.329\nSkew: 0.092 Prob(JB): 0.515\nKurtosis: 1.554 Cond. No. 19.2\n==================================================== ============================<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>Katsay\u0131<\/strong> s\u00fctunundan regresyon katsay\u0131lar\u0131n\u0131 g\u00f6rebilir ve a\u015fa\u011f\u0131daki uygun regresyon denklemini yazabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Puan = 65,334 + 1,9824*(saat)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu, \u00e7al\u0131\u015f\u0131lan her ek saatin ortalama <strong>1,9824<\/strong> puanl\u0131k s\u0131nav puan\u0131 art\u0131\u015f\u0131yla ili\u015fkili oldu\u011fu anlam\u0131na gelir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Orijinal de\u011feri olan <strong>65.334<\/strong> bize s\u0131f\u0131r saat ders \u00e7al\u0131\u015fan bir \u00f6\u011frencinin ortalama beklenen s\u0131nav puan\u0131n\u0131 anlat\u0131r.<\/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.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin 10 saat ders \u00e7al\u0131\u015fan bir \u00f6\u011frencinin s\u0131nav puan\u0131n\u0131n <strong>85.158<\/strong> olmas\u0131 gerekir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Puan = 65,334 + 1,9824*(10) = 85,158<\/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>P(&gt;|t|):<\/strong> Model katsay\u0131lar\u0131yla ili\u015fkili p de\u011feridir. <em>Saatlere<\/em> ili\u015fkin p de\u011feri (0,000) 0,05&#8217;ten 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>R-kare:<\/strong> Bu bize s\u0131nav puanlar\u0131ndaki de\u011fi\u015fim y\u00fczdesinin \u00e7al\u0131\u015f\u0131lan saat say\u0131s\u0131yla a\u00e7\u0131klanabilece\u011fini s\u00f6yler. 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>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>2.25e-06<\/strong> ) bize regresyon modelinin genel \u00f6nemini, yani modeldeki yorday\u0131c\u0131 de\u011fi\u015fkenlerin varyasyonu a\u00e7\u0131klamada 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<h2> <span style=\"color: #000000;\"><strong>3. Ad\u0131m: En uygun \u00e7izgiyi g\u00f6rselle\u015ftirin<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Son olarak, ger\u00e7ek veri noktalar\u0131na uygun regresyon \u00e7izgisini g\u00f6rselle\u015ftirmek i\u00e7in <strong>matplotlib<\/strong> veri g\u00f6rselle\u015ftirme paketini kullanabiliriz:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008000;\">import<\/span> matplotlib. <span style=\"color: #3366ff;\">pyplot<\/span> <span style=\"color: #008000;\">as<\/span> plt\n<\/span>\n#find line of best fit\n<span style=\"color: #000000;\">a, b = np. <span style=\"color: #3366ff;\">polyfit<\/span> (df[' <span style=\"color: #ff0000;\">hours<\/span> '], df[' <span style=\"color: #ff0000;\">score<\/span> '], <span style=\"color: #008000;\">1<\/span> )\n<\/span>\n#add points to plot\n<span style=\"color: #000000;\">plt. <span style=\"color: #3366ff;\">scatter<\/span> (df[' <span style=\"color: #ff0000;\">hours<\/span> '], df[' <span style=\"color: #ff0000;\">score<\/span> '], color=' <span style=\"color: #ff0000;\">purple<\/span> ')\n<\/span>\n#add line of best fit to plot\n<span style=\"color: #000000;\">plt. <span style=\"color: #3366ff;\">plot<\/span> (df[' <span style=\"color: #ff0000;\">hours<\/span> '], a*df[' <span style=\"color: #ff0000;\">hours<\/span> ']+b)\n<\/span>\n#add fitted regression equation to plot\n<span style=\"color: #000000;\">plt. <span style=\"color: #3366ff;\">text<\/span> ( <span style=\"color: #008000;\">1<\/span> , <span style=\"color: #008000;\">90<\/span> , 'y = ' + '{:.3f}'.format(b) + ' + {:.3f}'.format(a) + 'x', size= <span style=\"color: #008000;\">12<\/span> )\n\n<span style=\"color: #008080;\">#add axis labels\n<\/span>plt. <span style=\"color: #3366ff;\">xlabel<\/span> (' <span style=\"color: #ff0000;\">Hours Studied<\/span> ')\nplt. <span style=\"color: #3366ff;\">ylabel<\/span> (' <span style=\"color: #ff0000;\">Exam Score<\/span> ')\n<\/span><\/span><\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-29456 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/ligne11.jpg\" alt=\"\" width=\"502\" height=\"385\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Mor noktalar ger\u00e7ek veri noktalar\u0131n\u0131 temsil eder ve mavi \u00e7izgi ise tak\u0131lan regresyon \u00e7izgisini temsil eder.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ayr\u0131ca uygun regresyon denklemini grafi\u011fin sol \u00fcst k\u00f6\u015fesine eklemek i\u00e7in <strong>plt.text()<\/strong> fonksiyonunu kulland\u0131k.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Grafi\u011fe bak\u0131ld\u0131\u011f\u0131nda, uygun regresyon \u00e7izgisinin <strong>saat<\/strong> de\u011fi\u015fkeni ile <strong>puan<\/strong> de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkiyi olduk\u00e7a iyi yakalad\u0131\u011f\u0131 g\u00f6r\u00fclmektedir.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimlerde Python&#8217;da di\u011fer genel g\u00f6revlerin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/lojistik-regresyon-pitonu\/\" target=\"_blank\" rel=\"noopener\">Python&#8217;da Lojistik Regresyon Nas\u0131l Ger\u00e7ekle\u015ftirilir<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/ustel-regresyon-pitonu\/\" target=\"_blank\" rel=\"noopener\">Python&#8217;da \u00dcstel Regresyon Nas\u0131l Ger\u00e7ekle\u015ftirilir<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/pythonda-aic\/\" target=\"_blank\" rel=\"noopener\">Python&#8217;da regresyon modellerinin AIC&#8217;si nas\u0131l hesaplan\u0131r<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>S\u0131radan en k\u00fc\u00e7\u00fck kareler (OLS) regresyonu, bir veya daha fazla yorday\u0131c\u0131 de\u011fi\u015fken ile bir yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkiyi en iyi tan\u0131mlayan do\u011fruyu bulmam\u0131z\u0131 sa\u011flayan bir y\u00f6ntemdir. Bu y\u00f6ntem a\u015fa\u011f\u0131daki denklemi bulmam\u0131z\u0131 sa\u011flar: \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-3560","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>Python&#039;da OLS Regresyon Nas\u0131l Ger\u00e7ekle\u015ftirilir (\u00d6rnekle) - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde Python&#039;da s\u0131radan en k\u00fc\u00e7\u00fck kareler (OLS) regresyonunun nas\u0131l ger\u00e7ekle\u015ftirilece\u011fine ili\u015fkin ad\u0131m ad\u0131m bir \u00f6rnek sunulmaktad\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\/ols-regresyon-pitonu\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Python&#039;da OLS Regresyon Nas\u0131l Ger\u00e7ekle\u015ftirilir (\u00d6rnekle) - 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