{"id":1206,"date":"2023-07-27T07:20:18","date_gmt":"2023-07-27T07:20:18","guid":{"rendered":"https:\/\/statorials.org\/tr\/pythonda-ana-bilesenlerin-regresyonu\/"},"modified":"2023-07-27T07:20:18","modified_gmt":"2023-07-27T07:20:18","slug":"pythonda-ana-bilesenlerin-regresyonu","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/pythonda-ana-bilesenlerin-regresyonu\/","title":{"rendered":"Python&#39;da temel bile\u015fen regresyon (ad\u0131m ad\u0131m)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Bir dizi <em>p<\/em> tahmin de\u011fi\u015fkeni ve bir yan\u0131t de\u011fi\u015fkeni verildi\u011finde, <a href=\"https:\/\/statorials.org\/tr\/coklu-dogrusal-regresyon\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u00e7oklu do\u011frusal regresyon<\/a> , kalan kareler toplam\u0131n\u0131 (RSS) en aza indirmek i\u00e7in en k\u00fc\u00e7\u00fck kareler olarak bilinen bir y\u00f6ntemi kullan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>RSS = \u03a3(y <sub>ben<\/sub> \u2013 \u0177 <sub>ben<\/sub> ) <sup>2<\/sup><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> : <em>Toplam<\/em> anlam\u0131na gelen bir Yunan sembol\u00fc<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>y <sub>i<\/sub><\/strong> : <sup>i&#8217;inci<\/sup> g\u00f6zlem i\u00e7in ger\u00e7ek yan\u0131t de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u0177 <sub>i<\/sub><\/strong> : \u00c7oklu do\u011frusal regresyon modeline dayal\u0131 olarak tahmin edilen yan\u0131t de\u011feri<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Ancak yorday\u0131c\u0131 de\u011fi\u015fkenler y\u00fcksek d\u00fczeyde korelasyona sahip oldu\u011funda<\/span> <a href=\"https:\/\/statorials.org\/tr\/coklu-baglanti-regresyonu\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u00e7oklu do\u011frusall\u0131k<\/a> <span style=\"color: #000000;\">bir sorun haline gelebilir. Bu, model katsay\u0131 tahminlerini g\u00fcvenilmez hale getirebilir ve y\u00fcksek varyans sergileyebilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu sorunu \u00f6nlemenin bir yolu, orijinal <em>p<\/em> tahmincilerinin <em>M<\/em> <a href=\"https:\/\/statorials.org\/tr\/temel-bilesenler-regresyonu\/\" target=\"_blank\" rel=\"noopener noreferrer\">do\u011frusal kombinasyonunu (&#8220;temel bile\u015fenler&#8221; olarak adland\u0131r\u0131l\u0131r) bulan ve ard\u0131ndan temel bile\u015fenleri tahminci olarak kullanan do\u011frusal bir regresyon modeline uymak i\u00e7in en k\u00fc\u00e7\u00fck kareleri kullanan temel bile\u015fenler regresyonunu<\/a> kullanmakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu e\u011fitimde Python&#8217;da temel bile\u015fenlerin regresyonunun 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 i\u00e7e aktar\u0131n<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">\u0130lk olarak Python&#8217;da temel bile\u015fen regresyonunu (PCR) ger\u00e7ekle\u015ftirmek i\u00e7in gereken paketleri i\u00e7e aktaraca\u011f\u0131z:<\/span><\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n<span style=\"color: #008000;\">import<\/span> pandas <span style=\"color: #008000;\">as<\/span> pd\n<span style=\"color: #008000;\">import<\/span> matplotlib. <span style=\"color: #3366ff;\">pyplot<\/span> <span style=\"color: #008000;\">as<\/span> plt\n<span style=\"color: #008000;\">from<\/span> sklearn. <span style=\"color: #3366ff;\">preprocessing<\/span> <span style=\"color: #008000;\">import<\/span> scale \n<span style=\"color: #008000;\">from<\/span> sklearn <span style=\"color: #008000;\">import<\/span> model_selection\n<span style=\"color: #008000;\">from<\/span> sklearn. <span style=\"color: #3366ff;\">model_selection<\/span> <span style=\"color: #008000;\">import<\/span> RepeatedKFold\n<span style=\"color: #008000;\">from<\/span> sklearn.model_selection <span style=\"color: #008000;\">import<\/span> train_test_split\n<span style=\"color: #008000;\">from<\/span> sklearn. PCA <span style=\"color: #008000;\">import<\/span> <span style=\"color: #3366ff;\">decomposition<\/span>\n<span style=\"color: #008000;\">from<\/span> sklearn. <span style=\"color: #3366ff;\">linear_model<\/span> <span style=\"color: #008000;\">import<\/span> LinearRegression\n<span style=\"color: #008000;\">from<\/span> sklearn. <span style=\"color: #3366ff;\">metrics<\/span> <span style=\"color: #008000;\">import<\/span> mean_squared_error\n<\/strong><\/span><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>2. Ad\u0131m: Verileri y\u00fckleyin<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnek i\u00e7in <strong>mtcars<\/strong> ad\u0131 verilen ve 33 farkl\u0131 araba hakk\u0131nda bilgi i\u00e7eren bir veri k\u00fcmesi kullanaca\u011f\u0131z. Yan\u0131t de\u011fi\u015fkeni olarak <strong>hp&#8217;yi<\/strong> ve yorday\u0131c\u0131lar olarak a\u015fa\u011f\u0131daki de\u011fi\u015fkenleri kullanaca\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;\"><span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod bu veri k\u00fcmesinin nas\u0131l y\u00fcklenip g\u00f6r\u00fcnt\u00fclenece\u011fini g\u00f6sterir:<\/span><\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#define URL where data is located\n<\/span>url = \"https:\/\/raw.githubusercontent.com\/Statorials\/Python-Guides\/main\/mtcars.csv\"\n\n<span style=\"color: #008080;\">#read in data\n<\/span>data_full = pd. <span style=\"color: #3366ff;\">read_csv<\/span> (url)\n\n<span style=\"color: #008080;\">#select subset of data\n<\/span>data = data_full[[\"mpg\", \"disp\", \"drat\", \"wt\", \"qsec\", \"hp\"]]\n\n<span style=\"color: #008080;\">#view first six rows of data\n<\/span>data[0:6]\n\n\n        mpg disp drat wt qsec hp\n0 21.0 160.0 3.90 2.620 16.46 110\n1 21.0 160.0 3.90 2.875 17.02 110\n2 22.8 108.0 3.85 2.320 18.61 93\n3 21.4 258.0 3.08 3.215 19.44 110\n4 18.7 360.0 3.15 3.440 17.02 175\n5 18.1 225.0 2.76 3.460 20.22 105<\/strong><\/span><\/pre>\n<h3> <strong>Ad\u0131m 3: PCR modelini ayarlay\u0131n<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod PCR modelinin bu verilere nas\u0131l s\u0131\u011fd\u0131r\u0131laca\u011f\u0131n\u0131 g\u00f6sterir. A\u015fa\u011f\u0131dakilere dikkat et:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>pca.fit_transform(scale(X))<\/strong> : Bu, Python&#8217;a tahmin de\u011fi\u015fkenlerinin her birinin ortalamas\u0131 0 ve standart sapmas\u0131 1 olacak \u015fekilde \u00f6l\u00e7eklendirilmesi gerekti\u011fini s\u00f6yler. Bu, hi\u00e7bir tahmin de\u011fi\u015fkeninin modelde \u00e7ok fazla etkiye sahip olmamas\u0131n\u0131 sa\u011flar. bu meydana gelir. farkl\u0131 birimlerle \u00f6l\u00e7\u00fclecektir.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>cv = RepeatedKFold()<\/strong> : Bu, Python&#8217;a 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. Bu \u00f6rnek i\u00e7in k = 10 kat se\u00e7iyoruz, bu 3 kez tekrarlan\u0131yor.<\/span> <\/li>\n<\/ul>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#define predictor and response variables\n<\/span>X = data[[\"mpg\", \"disp\", \"drat\", \"wt\", \"qsec\"]]\ny = data[[\"hp\"]]\n\n<span style=\"color: #008080;\">#scale predictor variables\n<\/span>pca = pca()\nX_reduced = pca. <span style=\"color: #3366ff;\">fit_transform<\/span> ( <span style=\"color: #3366ff;\">scale<\/span> (X))\n\n<span style=\"color: #008080;\">#define cross validation method\n<\/span>cv = RepeatedKFold(n_splits= <span style=\"color: #008000;\">10<\/span> , n_repeats= <span style=\"color: #008000;\">3<\/span> , random_state= <span style=\"color: #008000;\">1<\/span> )\n\nregr = LinearRegression()\nmse = []\n\n<span style=\"color: #008080;\"># Calculate MSE with only the intercept\n<\/span>score = -1*model_selection. <span style=\"color: #3366ff;\">cross_val_score<\/span> (regr,\n           n.p. <span style=\"color: #3366ff;\">ones<\/span> ((len(X_reduced),1)), y, cv=cv,\n           scoring=' <span style=\"color: #008000;\">neg_mean_squared_error<\/span> '). <span style=\"color: #3366ff;\">mean<\/span> ()    \nmse. <span style=\"color: #3366ff;\">append<\/span> (score)\n\n<span style=\"color: #008080;\"># Calculate MSE using cross-validation, adding one component at a time\n<\/span><span style=\"color: #008000;\">for<\/span> i <span style=\"color: #008000;\">in<\/span> np. <span style=\"color: #3366ff;\">arange<\/span> (1, 6):\n    score = -1*model_selection. <span style=\"color: #3366ff;\">cross_val_score<\/span> (regr,\n               X_reduced[:,:i], y, cv=cv, scoring=' <span style=\"color: #008000;\">neg_mean_squared_error<\/span> '). <span style=\"color: #3366ff;\">mean<\/span> ()\n    mse. <span style=\"color: #3366ff;\">append<\/span> (score)\n    \n<span style=\"color: #008080;\"># Plot cross-validation results    \n<\/span>plt. <span style=\"color: #3366ff;\">plot<\/span> (mse)\nplt. <span style=\"color: #3366ff;\">xlabel<\/span> ('Number of Principal Components')\nplt. <span style=\"color: #3366ff;\">ylabel<\/span> ('MSE')\nplt. <span style=\"color: #3366ff;\">title<\/span> ('hp')<\/strong><\/span> <\/pre>\n<h3><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11950 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/pcrpython1.png\" alt=\"Python'da Temel Bile\u015fen Regresyonu\" width=\"424\" height=\"285\" srcset=\"\" sizes=\"auto, \"><\/h3>\n<p> <span style=\"color: #000000;\">Grafik, x ekseni boyunca ana bile\u015fenlerin say\u0131s\u0131n\u0131 ve y ekseni boyunca MSE (ortalama kare hatas\u0131) testini g\u00f6r\u00fcnt\u00fcler.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Grafikten, testin MSE&#8217;sinin iki temel bile\u015fen eklendi\u011finde azald\u0131\u011f\u0131n\u0131 ancak ikiden fazla temel bile\u015fen ekledik\u00e7e artmaya ba\u015flad\u0131\u011f\u0131n\u0131 g\u00f6rebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu nedenle optimal model yaln\u0131zca ilk iki temel bile\u015feni i\u00e7erir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Her bir temel bile\u015feni modele ekleyerek a\u00e7\u0131klanan yan\u0131t de\u011fi\u015fkenindeki varyans y\u00fczdesini hesaplamak i\u00e7in a\u015fa\u011f\u0131daki kodu da kullanabiliriz:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong>n.p. <span style=\"color: #3366ff;\">cumsum<\/span> (np. <span style=\"color: #3366ff;\">round<\/span> (pca. <span style=\"color: #3366ff;\">explained_variance_ratio_<\/span> , decimals= <span style=\"color: #008000;\">4<\/span> )* <span style=\"color: #008000;\">100<\/span> )\n\narray([69.83, 89.35, 95.88, 98.95, 99.99])\n<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131dakileri g\u00f6rebiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Yaln\u0131zca ilk temel bile\u015feni kullanarak yan\u0131t de\u011fi\u015fkenindeki varyasyonun <strong>%69,83&#8217;\u00fcn\u00fc<\/strong> a\u00e7\u0131klayabiliriz.<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0130kinci temel bile\u015feni ekleyerek yan\u0131t de\u011fi\u015fkenindeki varyasyonun <strong>%89,35&#8217;ini<\/strong> a\u00e7\u0131klayabiliriz.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Daha fazla temel bile\u015fen kullanarak hala daha fazla varyans\u0131 a\u00e7\u0131klayabilece\u011fimizi unutmay\u0131n, ancak ikiden fazla temel bile\u015fen eklemenin asl\u0131nda a\u00e7\u0131klanan varyans y\u00fczdesini \u00e7ok fazla art\u0131rmad\u0131\u011f\u0131n\u0131 g\u00f6rebiliriz.<\/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 iki temel bile\u015fenli PCR modelini 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 PCR modelinin iki temel bile\u015fenle nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#split the dataset into training (70%) and testing (30%) sets\n<\/span>X_train,X_test,y_train,y_test = <span style=\"color: #3366ff;\">train_test_split<\/span> (X,y,test_size= <span style=\"color: #008000;\">0.3<\/span> , random_state= <span style=\"color: #008000;\">0<\/span> ) \n\n<span style=\"color: #008080;\">#scale the training and testing data\n<\/span>X_reduced_train = pca. <span style=\"color: #3366ff;\">fit_transform<\/span> ( <span style=\"color: #3366ff;\">scale<\/span> (X_train))\nX_reduced_test = pca. <span style=\"color: #3366ff;\">transform<\/span> ( <span style=\"color: #3366ff;\">scale<\/span> (X_test))[:,:1]\n\n<span style=\"color: #008080;\">#train PCR model on training data \n<\/span>regr = LinearRegression()\nreg. <span style=\"color: #3366ff;\">fit<\/span> (X_reduced_train[:,:1], y_train)\n\n<span style=\"color: #008080;\">#calculate RMSE\n<\/span>pred = regr. <span style=\"color: #3366ff;\">predict<\/span> (X_reduced_test)\nn.p. <span style=\"color: #3366ff;\">sqrt<\/span> ( <span style=\"color: #3366ff;\">mean_squared_error<\/span> (y_test, pred))\n\n40.2096\n<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">RMSE testinin <strong>40.2096<\/strong> \u00e7\u0131kt\u0131\u011f\u0131n\u0131 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;\">Bu \u00f6rnekte kullan\u0131lan Python kodunun tamam\u0131n\u0131 <a href=\"https:\/\/github.com\/Statorials\/Python-Guides\/blob\/main\/principal_components_regression.py\" target=\"_blank\" rel=\"noopener noreferrer\">burada<\/a> bulabilirsiniz.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bir dizi p tahmin de\u011fi\u015fkeni ve bir yan\u0131t de\u011fi\u015fkeni verildi\u011finde, \u00e7oklu do\u011frusal regresyon , kalan kareler toplam\u0131n\u0131 (RSS) en aza indirmek i\u00e7in en k\u00fc\u00e7\u00fck kareler olarak bilinen bir y\u00f6ntemi kullan\u0131r: RSS = \u03a3(y ben \u2013 \u0177 ben ) 2 Alt\u0131n: \u03a3 : Toplam anlam\u0131na gelen bir Yunan sembol\u00fc y i : i&#8217;inci g\u00f6zlem i\u00e7in ger\u00e7ek [&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-1206","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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