{"id":883,"date":"2023-07-28T10:48:49","date_gmt":"2023-07-28T10:48:49","guid":{"rendered":"https:\/\/statorials.org\/tr\/dogrusal-regresyon-pitonu\/"},"modified":"2023-07-28T10:48:49","modified_gmt":"2023-07-28T10:48:49","slug":"dogrusal-regresyon-pitonu","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/dogrusal-regresyon-pitonu\/","title":{"rendered":"Python'da do\u011frusal regresyon i\u0307\u00e7in tam bir k\u0131lavuz"},"content":{"rendered":"

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Do\u011frusal regresyon,<\/strong> bir veya daha fazla yorday\u0131c\u0131 de\u011fi\u015fken ile bir yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkiyi anlamak i\u00e7in kullanabilece\u011fimiz bir y\u00f6ntemdir.<\/span><\/p>\n

Bu e\u011fitimde Python’da do\u011frusal regresyonun nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r.<\/span><\/p>\n

\u00d6rnek: Python’da do\u011frusal regresyon<\/strong><\/span><\/h3>\n

\u00c7al\u0131\u015fmak i\u00e7in harcanan saatlerin ve al\u0131nan uygulama s\u0131navlar\u0131n\u0131n say\u0131s\u0131n\u0131n, \u00f6\u011frencinin belirli bir s\u0131navda ald\u0131\u011f\u0131 notu etkileyip etkilemedi\u011fini bilmek istedi\u011fimizi varsayal\u0131m.<\/span><\/p>\n

Bu ili\u015fkiyi ara\u015ft\u0131rmak i\u00e7in Python’da \u00e7oklu do\u011frusal regresyon ger\u00e7ekle\u015ftirmek \u00fczere a\u015fa\u011f\u0131daki ad\u0131mlar\u0131 uygulayabiliriz.<\/span><\/p>\n

Ad\u0131m 1: Verileri girin.<\/strong><\/span><\/p>\n

\u00d6ncelikle veri k\u00fcmemizi tutacak bir pandas DataFrame olu\u015fturaca\u011f\u0131z:<\/span><\/p>\n

 import<\/span> pandas as<\/span> pd\n\n#create data<\/span>\ndf = pd.DataFrame({'hours': [1, 2, 2, 4, 2, 1, 5, 4, 2, 4, 4, 3, 6, 5, 3, 4, 6, 2, 1, 2],\n                   'exams': [1, 3, 3, 5, 2, 2, 1, 1, 0, 3, 4, 3, 2, 4, 4, 4, 5, 1, 0, 1],\n                   'score': [76, 78, 85, 88, 72, 69, 94, 94, 88, 92, 90, 75, 96, 90, 82, 85, 99, 83, 62, 76]})\n\n#view data<\/span> \ndf\n\n        hours exam score\n0 1 1 76\n1 2 3 78\n2 2 3 85\n3 4 5 88\n4 2 2 72\n5 1 2 69\n6 5 1 94\n7 4 1 94\n8 2 0 88\n9 4 3 92\n10 4 4 90\n11 3 3 75\n12 6 2 96\n13 5 4 90\n14 3 4 82\n15 4 4 85\n16 6 5 99\n17 2 1 83\n18 1 0 62\n19 2 1 76\n<\/strong><\/pre>\n
 Ad\u0131m 2: Do\u011frusal regresyon ger\u00e7ekle\u015ftirin.<\/strong><\/span><\/p>\n
 Daha sonra, tahmin de\u011fi\u015fkenleri olarak “saatler” ve “s\u0131navlar”\u0131 ve yan\u0131t de\u011fi\u015fkeni olarak “puan”\u0131 kullanarak s\u0131radan bir en k\u00fc\u00e7\u00fck kareler regresyonu ger\u00e7ekle\u015ftirmek i\u00e7in statsmodels k\u00fct\u00fcphanesindeki OLS() i\u015flevini<\/a> kullanaca\u011f\u0131z:<\/span><\/p>\n
 import<\/span> statsmodels.api as<\/span> sm\n\n#define response variable\n<\/span>y = df['score']\n\n#define predictor variables\n<\/span>x = df[['hours', 'exams']]\n\n#add constant to predictor variables\n<\/span>x = sm.add_constant(x)\n\n#fit linear regression model\n<\/span>model = sm.OLS(y, x).fit()\n\n#view model summary\n<\/span>print(model.summary())\n\n                            OLS Regression Results                            \n==================================================== ============================\nDept. Variable: R-squared score: 0.734\nModel: OLS Adj. R-squared: 0.703\nMethod: Least Squares F-statistic: 23.46\nDate: Fri, 24 Jul 2020 Prob (F-statistic): 1.29e-05\nTime: 13:20:31 Log-Likelihood: -60.354\nNo. Observations: 20 AIC: 126.7\nDf Residuals: 17 BIC: 129.7\nDf Model: 2                                         \nCovariance Type: non-robust                                         \n==================================================== ============================\n                 coef std err t P>|t| [0.025 0.975]\n-------------------------------------------------- ----------------------------\nconst 67.6735 2.816 24.033 0.000 61.733 73.614\nhours 5.5557 0.899 6.179 0.000 3.659 7.453\nexams -0.6017 0.914 -0.658 0.519 -2.531 1.327\n==================================================== ============================\nOmnibus: 0.341 Durbin-Watson: 1.506\nProb(Omnibus): 0.843 Jarque-Bera (JB): 0.196\nSkew: -0.216 Prob(JB): 0.907\nKurtosis: 2,782 Cond. No. 10.8\n==================================================== ============================\n<\/strong><\/pre>\n
 Ad\u0131m 3: Sonu\u00e7lar\u0131 yorumlay\u0131n.<\/strong><\/span><\/p>\n
 Sonu\u00e7taki en alakal\u0131 say\u0131lar\u0131 nas\u0131l yorumlayaca\u011f\u0131n\u0131z a\u015fa\u011f\u0131da a\u00e7\u0131klanm\u0131\u015ft\u0131r:<\/span><\/p>\n
 R kare:<\/strong> 0,734<\/strong> . Buna belirleme katsay\u0131s\u0131 denir. Bu, yorday\u0131c\u0131 de\u011fi\u015fkenler taraf\u0131ndan a\u00e7\u0131klanabilen yan\u0131t de\u011fi\u015fkenindeki varyans\u0131n oran\u0131d\u0131r. Bu \u00f6rnekte s\u0131nav puanlar\u0131ndaki farkl\u0131l\u0131\u011f\u0131n %73,4’\u00fc \u00e7al\u0131\u015f\u0131lan saat ve girilen haz\u0131rl\u0131k s\u0131nav\u0131 say\u0131s\u0131yla a\u00e7\u0131klanmaktad\u0131r.<\/span><\/p>\n
 F istatisti\u011fi: 23.46<\/strong> . Bu, regresyon modelinin genel F istatisti\u011fidir.<\/span><\/p>\n
 Olas\u0131l\u0131k (F istatisti\u011fi): 1.29e-05.<\/strong> Bu, genel F istatisti\u011fiyle ili\u015fkili p de\u011feridir. Bu bize regresyon modelinin bir b\u00fct\u00fcn olarak istatistiksel olarak anlaml\u0131 olup olmad\u0131\u011f\u0131n\u0131 s\u00f6yler. Ba\u015fka bir deyi\u015fle, bize iki yorday\u0131c\u0131 de\u011fi\u015fkenin birle\u015fiminin yan\u0131t de\u011fi\u015fkeni ile istatistiksel olarak anlaml\u0131 bir ili\u015fkiye sahip olup olmad\u0131\u011f\u0131n\u0131 s\u00f6yler. Bu durumda p de\u011feri 0,05’ten k\u00fc\u00e7\u00fckt\u00fcr; bu durum yorday\u0131c\u0131 de\u011fi\u015fkenler olan \u201c\u00e7al\u0131\u015fma saatleri\u201d ve \u201cgirilen haz\u0131rl\u0131k s\u0131navlar\u0131\u201dn\u0131n birle\u015fiminin s\u0131nav puan\u0131yla istatistiksel olarak anlaml\u0131 bir ili\u015fkiye sahip oldu\u011funu g\u00f6stermektedir.<\/span><\/p>\n
 katsay\u0131:<\/strong> Her yorday\u0131c\u0131 de\u011fi\u015fkenin katsay\u0131lar\u0131, di\u011fer yorday\u0131c\u0131 de\u011fi\u015fkenin sabit kald\u0131\u011f\u0131n\u0131 varsayarak, bize yan\u0131t de\u011fi\u015fkeninde beklenen ortalama de\u011fi\u015fikli\u011fi s\u00f6yler. \u00d6rne\u011fin, al\u0131nan deneme s\u0131navlar\u0131n\u0131n sabit kald\u0131\u011f\u0131 varsay\u0131larak, ders \u00e7al\u0131\u015fmak i\u00e7in harcanan her ek saat i\u00e7in ortalama s\u0131nav puan\u0131n\u0131n 5,56<\/strong> artmas\u0131 beklenir.<\/span><\/p>\n
 Buna ba\u015fka bir a\u00e7\u0131dan da bakabiliriz: \u00d6\u011frenci A ve \u00d6\u011frenci B ayn\u0131 say\u0131da haz\u0131rl\u0131k s\u0131nav\u0131na girerse ancak \u00d6\u011frenci A bir saat daha uzun \u00e7al\u0131\u015f\u0131rsa, \u00d6\u011frenci A, \u00d6\u011frenci B’den 5,56<\/strong> puan daha y\u00fcksek puan almal\u0131d\u0131r.<\/span><\/p>\n
 Kesi\u015fme katsay\u0131s\u0131n\u0131, ders saati \u00e7al\u0131\u015fmayan ve haz\u0131rl\u0131k s\u0131nav\u0131na girmeyen bir \u00f6\u011frenci i\u00e7in beklenen s\u0131nav puan\u0131n\u0131n 67,67<\/strong> oldu\u011fu \u015feklinde yorumluyoruz.<\/span><\/p>\n
 P>|t|.<\/strong> Bireysel p de\u011ferleri bize her bir yorday\u0131c\u0131 de\u011fi\u015fkenin istatistiksel olarak anlaml\u0131 olup olmad\u0131\u011f\u0131n\u0131 s\u00f6yler. \u201cSaatler\u201din istatistiksel olarak anlaml\u0131 (p=0,00), \u201cs\u0131navlar\u201d\u0131n ise anlaml\u0131 oldu\u011funu g\u00f6r\u00fcyoruz.  <\/strong> (p = 0,52) \u03b1 = 0,05’te istatistiksel olarak anlaml\u0131 de\u011fildir. \u201cS\u0131navlar\u201d terimi istatistiksel olarak anlaml\u0131 olmad\u0131\u011f\u0131ndan onu modelden \u00e7\u0131karmaya karar verebiliriz.<\/span><\/p>\n
 Tahmini regresyon denklemi:<\/strong> A\u015fa\u011f\u0131daki tahmini regresyon denklemini olu\u015fturmak i\u00e7in model \u00e7\u0131kt\u0131s\u0131ndaki katsay\u0131lar\u0131 kullanabiliriz:<\/span><\/p>\n
 s\u0131nav puan\u0131 = 67,67 + 5,56*(saat) \u2013 0,60*(haz\u0131rl\u0131k s\u0131navlar\u0131)<\/strong><\/span><\/p>\n
 Bu tahmini regresyon denklemini, bir \u00f6\u011frencinin \u00e7al\u0131\u015fma saati ve girdi\u011fi deneme s\u0131navlar\u0131n\u0131n say\u0131s\u0131na ba\u011fl\u0131 olarak beklenen s\u0131nav puan\u0131n\u0131 hesaplamak i\u00e7in kullanabiliriz. \u00d6rne\u011fin \u00fc\u00e7 saat \u00e7al\u0131\u015f\u0131p haz\u0131rl\u0131k s\u0131nav\u0131na giren bir \u00f6\u011frencinin notunun 83,75<\/strong> olmas\u0131 gerekir:<\/span><\/p>\n
 Ge\u00e7mi\u015f haz\u0131rl\u0131k s\u0131navlar\u0131n\u0131n istatistiksel olarak anlaml\u0131 olmamas\u0131 nedeniyle (p = 0,52), genel modele herhangi bir iyile\u015ftirme sa\u011flamamas\u0131 nedeniyle bunlar\u0131 kald\u0131rmaya karar verebilece\u011fimizi unutmay\u0131n. Bu durumda, yorday\u0131c\u0131 de\u011fi\u015fken olarak yaln\u0131zca \u00e7al\u0131\u015f\u0131lan saatleri kullanarak basit bir do\u011frusal regresyon ger\u00e7ekle\u015ftirebiliriz.<\/span><\/p>\n
 Ad\u0131m 4: Model varsay\u0131mlar\u0131n\u0131 do\u011frulay\u0131n.<\/strong><\/span><\/p>\n
 Do\u011frusal bir regresyon ger\u00e7ekle\u015ftirdikten sonra, regresyon modelinin sonu\u00e7lar\u0131n\u0131n g\u00fcvenilir oldu\u011fundan emin olmak i\u00e7in \u00e7e\u015fitli varsay\u0131mlar\u0131 kontrol etmek isteyebilirsiniz. Bu varsay\u0131mlar \u015funlar\u0131 i\u00e7erir:<\/span><\/p>\n
 Varsay\u0131m #1:<\/strong> Yorday\u0131c\u0131 de\u011fi\u015fkenler ile yan\u0131t de\u011fi\u015fkeni aras\u0131nda do\u011frusal bir ili\u015fki vard\u0131r.<\/span><\/p>\n