Bu teknik, verilere en iyi “uyan” \u00e7izgiyi bulur ve a\u015fa\u011f\u0131daki formu al\u0131r:<\/span><\/p>\n \u0177 = b 0<\/sub> + b 1<\/sub> x<\/strong><\/span><\/p>\n Alt\u0131n:<\/span><\/p>\n 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 Bu e\u011fitimde Python’da basit do\u011frusal regresyonun nas\u0131l ger\u00e7ekle\u015ftirilece\u011fine ili\u015fkin ad\u0131m ad\u0131m bir a\u00e7\u0131klama sa\u011flanmaktad\u0131r.<\/span><\/p>\n 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 A\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fken olarak saatleri<\/em> ve yan\u0131t de\u011fi\u015fkeni olarak muayene sonu\u00e7lar\u0131n\u0131<\/em> kullanarak basit bir do\u011frusal regresyon modeli uydurmaya \u00e7al\u0131\u015faca\u011f\u0131z.<\/span><\/p>\n A\u015fa\u011f\u0131daki kod Python’da bu sahte veri k\u00fcmesinin nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span><\/p>\n Basit bir do\u011frusal regresyon modeli kurmadan \u00f6nce, anlamak i\u00e7in \u00f6ncelikle verileri g\u00f6rselle\u015ftirmemiz gerekir.<\/span><\/p>\n \u0130lk olarak, saat<\/em> ve puan<\/em> aras\u0131ndaki ili\u015fkinin yakla\u015f\u0131k olarak do\u011frusal olmas\u0131n\u0131 sa\u011flamak istiyoruz \u00e7\u00fcnk\u00fc bu, basit do\u011frusal regresyonun temel varsay\u0131m\u0131d\u0131r<\/a> .<\/span><\/p>\n \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 Grafikten ili\u015fkinin do\u011frusal oldu\u011funu g\u00f6rebiliriz. Saat say\u0131s\u0131<\/em> artt\u0131k\u00e7a puan<\/em> da do\u011frusal olarak artma e\u011filimindedir.<\/span><\/p>\n Daha sonra s\u0131nav sonu\u00e7lar\u0131n\u0131n da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6rselle\u015ftirmek ve ayk\u0131r\u0131 de\u011ferleri<\/a> kontrol etmek i\u00e7in bir kutu grafi\u011fi olu\u015fturabiliriz. Python, varsay\u0131lan olarak 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 olan bir g\u00f6zlemi ayk\u0131r\u0131 de\u011fer olarak tan\u0131mlar.<\/span><\/p>\n Bir g\u00f6zlem ayk\u0131r\u0131 ise kutu grafi\u011finde k\u00fc\u00e7\u00fck bir daire g\u00f6r\u00fcnecektir:<\/span> <\/p>\n 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 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 saatleri<\/em> ve yan\u0131t de\u011fi\u015fkeni olarak puan\u0131<\/em> kullanarak basit bir do\u011frusal regresyon modeli uydurmaya devam edebiliriz:<\/span><\/p>\n Not: Regresyon modeline uyum sa\u011flamak i\u00e7in statsmodels k\u00fct\u00fcphanesindeki<\/span> OLS() fonksiyonunu<\/a> kullanaca\u011f\u0131z<\/strong><\/span> .<\/em><\/p>\n Model \u00f6zetinden uygun regresyon denkleminin \u015f\u00f6yle oldu\u011funu g\u00f6rebiliriz:<\/span><\/p>\n Puan = 65,334 + 1,9824*(saat)<\/strong><\/span><\/p>\n Bu, \u00e7al\u0131\u015f\u0131lan her ek saatin ortalama 1,9824<\/strong> puanl\u0131k s\u0131nav puan\u0131 art\u0131\u015f\u0131yla ili\u015fkili oldu\u011fu anlam\u0131na gelir. Ve 65.334’\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 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 85.158<\/strong> olmas\u0131 gerekir:<\/span><\/p>\n Puan = 65,334 + 1,9824*(10) = 85,158<\/strong><\/span><\/p>\n Model \u00f6zetinin geri kalan\u0131n\u0131 \u015fu \u015fekilde yorumlayabilirsiniz:<\/span><\/p>\n Basit do\u011frusal regresyon modelini verilere yerle\u015ftirdikten sonra son ad\u0131m, art\u0131k grafiklerin olu\u015fturulmas\u0131d\u0131r.<\/span><\/p>\n 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 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 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 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 D\u00f6rt parsel \u00fcretilir. Sa\u011f \u00fcst k\u00f6\u015fedeki, d\u00fczeltilmi\u015f arsaya kar\u015f\u0131 kalan arsad\u0131r. Bu grafikteki x ekseni, tahmin de\u011fi\u015fkeni noktalar\u0131n\u0131n<\/em> ger\u00e7ek de\u011ferlerini, y ekseni ise bu de\u011fere ili\u015fkin art\u0131k de\u011feri g\u00f6sterir.<\/span><\/p>\n Art\u0131klar\u0131n s\u0131f\u0131r etraf\u0131nda rastgele da\u011f\u0131lm\u0131\u015f gibi g\u00f6r\u00fcnmesi, de\u011fi\u015fen varyans\u0131n a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenle ilgili bir sorun olmad\u0131\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n\n
1. Ad\u0131m: Verileri y\u00fckleyin<\/b><\/span><\/h3>\n
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import<\/span> pandas as<\/span> pd<\/span>\n\n#create dataset<\/span>\ndf = pd. DataFrame<\/span> ({' hours<\/span> ': [1, 2, 4, 5, 5, 6, 6, 7, 8, 10, 11, 11, 12, 12, 14],\n ' score<\/span> ': [64, 66, 76, 73, 74, 81, 83, 82, 80, 88, 84, 82, 91, 93, 89]})\n \n\n#view first six rows of dataset\n<\/span>df[0:6]\n\n hours score\n0 1 64\n1 2 66\n2 4 76\n3 5 73\n4 5 74\n5 6 81\n<\/strong><\/pre>\n 2. Ad\u0131m: Verileri g\u00f6rselle\u015ftirin<\/b><\/span><\/h3>\n
import<\/span> matplotlib.pyplot as<\/span> plt\n\nplt. scatter<\/span> (df.hours, df.score)\nplt. title<\/span> (' Hours studied vs. Exam Score<\/span> ')\nplt. xlabel<\/span> (' Hours<\/span> ')\nplt. ylabel<\/span> (' Score<\/span> ')\nplt. show<\/span> ()\n<\/strong><\/pre>\n![\"Python'da](\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/simpleregpython1.png\")
<\/p>\n df. boxplot<\/span> (column=[' score<\/span> '])<\/strong> <\/pre>\n![\"Python'da](\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/simpleregpython2.png\")
<\/p>\n Ad\u0131m 3: Basit Do\u011frusal Regresyon Ger\u00e7ekle\u015ftirin<\/b><\/span><\/h3>\n
import<\/span> statsmodels.api as<\/span> sm\n\n#define response variable\n<\/span>y = df[' score<\/span> ']\n\n#define explanatory variable\n<\/span>x = df[[' hours<\/span> ']]\n\n#add constant to predictor variables\n<\/span>x = sm. add_constant<\/span> (x)\n\n#fit linear regression model\n<\/span>model = sm. OLS<\/span> (y,x). fit<\/span> ()\n\n#view model summary\n<\/span>print<\/span> ( 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: Mon, 26 Oct 2020 Prob (F-statistic): 2.25e-06\nTime: 15:51:45 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>|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==================================================== ============================<\/strong><\/pre>\n\n
Ad\u0131m 4: Art\u0131k Grafikler Olu\u015fturun<\/strong><\/span><\/h3>\n
#define figure size\n<\/span>fig = plt. figure<\/span> (figsize=(12.8))\n\n#produce residual plots\n<\/span>fig = sm.graphics. plot_regress_exog<\/span> (model, ' hours<\/span> ', fig=fig)\n<\/strong><\/pre>\n![\"Python'da](\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/simpleregpython3.png\")
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![\"Python'da](\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/simpleregpython4.png\")
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