<\/p>\n
Regresyon analizinde heteroskedastisite<\/a> , art\u0131klar\u0131n e\u015fit olmayan da\u011f\u0131l\u0131m\u0131n\u0131 ifade eder. Daha do\u011frusu, \u00f6l\u00e7\u00fclen de\u011ferler aral\u0131\u011f\u0131 boyunca art\u0131klar\u0131n da\u011f\u0131l\u0131m\u0131nda sistematik bir de\u011fi\u015fikli\u011fin oldu\u011fu durum budur.<\/span><\/p>\n De\u011fi\u015fken varyans bir sorundur \u00e7\u00fcnk\u00fc s\u0131radan en k\u00fc\u00e7\u00fck kareler (OLS) regresyonu, art\u0131klar\u0131n e\u015fvaryansl\u0131l\u0131\u011fa<\/em> sahip bir pop\u00fclasyondan geldi\u011fini varsayar, yani sabit varyans anlam\u0131na gelir.<\/span><\/p>\n Bir regresyon analizinde de\u011fi\u015fen varyans mevcut oldu\u011funda, analiz sonu\u00e7lar\u0131na inanmak zorla\u015f\u0131r.<\/span><\/p>\n Bir regresyon analizinde<\/a> heteroskedastisitenin mevcut olup olmad\u0131\u011f\u0131n\u0131 belirlemenin bir yolu Breusch-Pagan testi<\/a> kullanmakt\u0131r .<\/strong><\/span><\/p>\n Bu e\u011fitimde Python’da Breusch-Pagan testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r.<\/span><\/p>\n Bu \u00f6rnek i\u00e7in 10 basketbolcunun \u00f6zelliklerini a\u00e7\u0131klayan a\u015fa\u011f\u0131daki veri k\u00fcmesini kullanaca\u011f\u0131z:<\/span><\/p>\n Yan\u0131t de\u011fi\u015fkeni olarak puanlamay\u0131 ve a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenler olarak say\u0131lar, asistler ve ribaundlar\u0131 kullanarak \u00e7oklu do\u011frusal regresyon modelini uygulayaca\u011f\u0131z. Daha sonra regresyonda heteroskedastisitenin mevcut olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in Breusch-Pagan testi uygulayaca\u011f\u0131z.<\/span><\/p>\n Ad\u0131m 1: \u00c7oklu do\u011frusal regresyon modelini yerle\u015ftirin.<\/strong><\/span><\/p>\n \u0130lk olarak \u00e7oklu do\u011frusal regresyon modelini uygulayaca\u011f\u0131z:<\/span><\/p>\n Ad\u0131m 2: Breusch-Pagan testi yap\u0131n.<\/strong><\/span><\/p>\n Daha sonra, de\u011fi\u015fen varyans\u0131n mevcut olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in Breusch-Pagan testi uygulayaca\u011f\u0131z.<\/span><\/p>\n Breusch-Pagan testi a\u015fa\u011f\u0131daki bo\u015f ve alternatif hipotezleri kullan\u0131r:<\/span><\/p>\n S\u0131f\u0131r hipotezi (H 0<\/sub> ):<\/strong> Homoskedastisite mevcuttur.<\/span><\/p>\n Alternatif hipotez: (Ha):<\/strong> E\u015f varyans mevcut de\u011fil<\/em> (yani de\u011fi\u015fen varyans var)<\/span><\/p>\n Bu \u00f6rnekte testin Lagrange \u00e7arpan\u0131 istatisti\u011fi 6,004<\/strong> ve buna kar\u015f\u0131l\u0131k gelen p de\u011feri 0,1114’t\u00fcr<\/strong> . Bu p de\u011feri 0,05’ten k\u00fc\u00e7\u00fck olmad\u0131\u011f\u0131 i\u00e7in s\u0131f\u0131r hipotezini reddedemiyoruz. Regresyon modelinde de\u011fi\u015fen varyans\u0131n mevcut oldu\u011funu iddia edecek yeterli kan\u0131t\u0131m\u0131z yok.<\/span><\/p>\n \u00d6nceki \u00f6rnekte regresyon modelinde de\u011fi\u015fen varyans\u0131n olmad\u0131\u011f\u0131n\u0131 g\u00f6rm\u00fc\u015ft\u00fck.<\/span><\/p>\n Bununla birlikte, de\u011fi\u015fen varyans ger\u00e7ekten mevcut oldu\u011funda, durumu d\u00fczeltmenin \u00fc\u00e7 yayg\u0131n yolu vard\u0131r:<\/span><\/p>\n 1.<\/strong> Ba\u011f\u0131ml\u0131 de\u011fi\u015fkeni d\u00f6n\u00fc\u015ft\u00fcr\u00fcn.<\/strong> Heteroskedasticity’yi d\u00fczeltmenin bir yolu ba\u011f\u0131ml\u0131 de\u011fi\u015fkeni bir \u015fekilde d\u00f6n\u00fc\u015ft\u00fcrmektir. Yayg\u0131n bir d\u00f6n\u00fc\u015f\u00fcm, ba\u011f\u0131ml\u0131 de\u011fi\u015fkenin logunu almakt\u0131r.<\/span><\/p>\n \u00d6rnek: Python’da Breusch-Pagan testi<\/strong><\/span><\/h2>\n
import<\/span> numpy as<\/span> np\nimport<\/span> pandas as<\/span> pd\n\n#create dataset<\/span>\ndf = pd.DataFrame({'rating': [90, 85, 82, 88, 94, 90, 76, 75, 87, 86],\n 'points': [25, 20, 14, 16, 27, 20, 12, 15, 14, 19],\n 'assists': [5, 7, 7, 8, 5, 7, 6, 9, 9, 5],\n 'rebounds': [11, 8, 10, 6, 6, 9, 6, 10, 10, 7]})\n\n#view dataset\n<\/span>df\n\n\trating points assists rebounds\n0 90 25 5 11\n1 85 20 7 8\n2 82 14 7 10\n3 88 16 8 6\n4 94 27 5 6\n5 90 20 7 9\n6 76 12 6 6\n7 75 15 9 10\n8 87 14 9 10\n9 86 19 5 7<\/strong><\/pre>\n import<\/span> statsmodels.formula.api as<\/span> smf\n\n#fit regression model<\/span>\nfit = smf.ols('rating ~ points+assists+rebounds', data=df). fit<\/span> ()\n\n#view model summary\n<\/span>print<\/span> (fit.summary())\n<\/strong><\/pre>\n from<\/span> statsmodels.compat import<\/span> lzip\nimport<\/span> statsmodels.stats.api as<\/span> sms\n\n#perform Bresuch-Pagan test<\/span>\nnames = ['Lagrange multiplier statistic', 'p-value',\n 'f-value', 'f p-value']\ntest = sms.het_breuschpagan(fit.resid, fit.model.exog)\n\nlzip(names, test)\n\n[('Lagrange multiply statistic', 6.003951995818433),\n ('p-value', 0.11141811013399583),\n ('f-value', 3.004944880309618),\n ('f p-value', 0.11663863538255281)]<\/strong><\/pre>\n Heteroscedasticity Nas\u0131l Onar\u0131l\u0131r<\/strong><\/span><\/h2>\n