Bu varsay\u0131ma uyulmad\u0131\u011f\u0131 takdirde art\u0131klarda de\u011fi\u015fen varyans\u0131n<\/a> mevcut oldu\u011fu s\u00f6ylenir. Bu durumda regresyon sonu\u00e7lar\u0131 g\u00fcvenilmez hale gelir.<\/span><\/p>\n Bu sorunu \u00e7\u00f6zmenin bir yolu, a\u011f\u0131rl\u0131kl\u0131 en k\u00fc\u00e7\u00fck kareler regresyonunu<\/strong> kullanmakt\u0131r; bu regresyon, g\u00f6zlemlere<\/a> a\u011f\u0131rl\u0131klar atayarak, d\u00fc\u015f\u00fck hata varyans\u0131na sahip olanlar\u0131n, daha b\u00fcy\u00fck hata varyans\u0131na sahip g\u00f6zlemlere k\u0131yasla daha fazla bilgi i\u00e7erdiklerinden daha fazla a\u011f\u0131rl\u0131k almas\u0131n\u0131 sa\u011flar.<\/span><\/p>\n Bu e\u011fitimde, R’de a\u011f\u0131rl\u0131kl\u0131 en k\u00fc\u00e7\u00fck kareler regresyonunun nas\u0131l ger\u00e7ekle\u015ftirilece\u011fine ili\u015fkin ad\u0131m ad\u0131m bir \u00f6rnek sa\u011flanmaktad\u0131r.<\/span><\/p>\n A\u015fa\u011f\u0131daki kod, 16 \u00f6\u011frenci i\u00e7in \u00e7al\u0131\u015f\u0131lan saat say\u0131s\u0131n\u0131 ve ilgili s\u0131nav puan\u0131n\u0131 i\u00e7eren bir veri \u00e7er\u00e7evesi olu\u015fturur:<\/span><\/p>\n Daha sonra, tahmin de\u011fi\u015fkeni olarak saatleri ve yan\u0131t de\u011fi\u015fkeni<\/a> olarak puan\u0131 kullanan basit bir do\u011frusal regresyon modeline<\/a> uyum sa\u011flamak i\u00e7in lm()<\/strong> i\u015flevini kullanaca\u011f\u0131z:<\/span><\/p>\n Daha sonra, heteroskedastisiteyi g\u00f6rsel olarak kontrol etmek i\u00e7in art\u0131klar\u0131n ve uydurulmu\u015f de\u011ferlerin bir grafi\u011fini olu\u015fturaca\u011f\u0131z:<\/span> <\/p>\n Art\u0131klar\u0131n \u201ckoni\u201d \u015fekline sahip oldu\u011funu grafikten g\u00f6rebiliriz: grafik boyunca e\u015fit varyansla da\u011f\u0131lmazlar.<\/span><\/p>\n De\u011fi\u015fen varyansl\u0131l\u0131\u011f\u0131 resmi olarak test etmek i\u00e7in Breusch-Pagan testi yapabiliriz:<\/span><\/p>\n Breusch-Pagan testi a\u015fa\u011f\u0131daki bo\u015f ve alternatif<\/span> hipotezleri<\/a><\/span> kullan\u0131r:<\/p>\n Testin p de\u011feri 0,0466<\/strong> oldu\u011fundan s\u0131f\u0131r hipotezini reddedece\u011fiz ve de\u011fi\u015fen varyans\u0131n bu modelde bir sorun oldu\u011fu sonucuna varaca\u011f\u0131z.<\/span><\/p>\n De\u011fi\u015fen varyans mevcut oldu\u011fundan, a\u011f\u0131rl\u0131klar\u0131 daha d\u00fc\u015f\u00fck varyansa sahip g\u00f6zlemlerin daha fazla a\u011f\u0131rl\u0131k alaca\u011f\u0131 \u015fekilde ayarlayarak a\u011f\u0131rl\u0131kl\u0131 en k\u00fc\u00e7\u00fck kareler uygulayaca\u011f\u0131z:<\/span><\/p>\n Sonu\u00e7lardan, saat<\/em> yorday\u0131c\u0131s\u0131 de\u011fi\u015fkenine ili\u015fkin katsay\u0131 tahmininin biraz de\u011fi\u015fti\u011fini ve genel model uyumunun iyile\u015fti\u011fini g\u00f6rebiliriz.<\/span><\/p>\n A\u011f\u0131rl\u0131kland\u0131r\u0131lm\u0131\u015f en k\u00fc\u00e7\u00fck kareler modeli, orijinal basit do\u011frusal regresyon modelindeki 9,224’e<\/strong> k\u0131yasla 1,199’luk<\/strong> bir art\u0131k standart hataya sahiptir.<\/span><\/p>\n Bu, a\u011f\u0131rl\u0131kl\u0131 en k\u00fc\u00e7\u00fck kareler modelinin \u00fcretti\u011fi tahmin edilen de\u011ferlerin, basit do\u011frusal regresyon modelinin \u00fcretti\u011fi tahmin edilen de\u011ferlerle kar\u015f\u0131la\u015ft\u0131r\u0131ld\u0131\u011f\u0131nda ger\u00e7ek g\u00f6zlemlere \u00e7ok daha yak\u0131n oldu\u011funu g\u00f6sterir.<\/span><\/p>\n A\u011f\u0131rl\u0131kland\u0131r\u0131lm\u0131\u015f en k\u00fc\u00e7\u00fck kareler modeli ayn\u0131 zamanda orijinal basit do\u011frusal regresyon modelindeki 0,6296’ya<\/strong> k\u0131yasla 0,6762’lik<\/strong> bir R-kare de\u011ferine sahiptir.<\/span><\/p>\n Bu, a\u011f\u0131rl\u0131kl\u0131 en k\u00fc\u00e7\u00fck kareler modelinin, basit do\u011frusal regresyon modeline g\u00f6re s\u0131nav puanlar\u0131ndaki varyans\u0131 daha fazla a\u00e7\u0131klayabildi\u011fini g\u00f6sterir.<\/span><\/p>\n Bu \u00f6l\u00e7\u00fcmler, a\u011f\u0131rl\u0131kl\u0131 en k\u00fc\u00e7\u00fck kareler modelinin, basit do\u011frusal regresyon modeline k\u0131yasla verilere daha iyi uyum sa\u011flad\u0131\u011f\u0131n\u0131 g\u00f6stermektedir.<\/span><\/p>\n R’de basit do\u011frusal regresyon nas\u0131l ger\u00e7ekle\u015ftirilir<\/a> Do\u011frusal regresyonun temel varsay\u0131mlar\u0131ndan biri, art\u0131klar\u0131n , yorday\u0131c\u0131 de\u011fi\u015fkenin her d\u00fczeyinde e\u015fit varyansla da\u011f\u0131ld\u0131\u011f\u0131d\u0131r. Bu varsay\u0131ma e\u015f varyansl\u0131l\u0131k denir. Bu varsay\u0131ma uyulmad\u0131\u011f\u0131 takdirde art\u0131klarda de\u011fi\u015fen varyans\u0131n mevcut oldu\u011fu s\u00f6ylenir. Bu durumda regresyon sonu\u00e7lar\u0131 g\u00fcvenilmez hale gelir. Bu sorunu \u00e7\u00f6zmenin bir yolu, a\u011f\u0131rl\u0131kl\u0131 en k\u00fc\u00e7\u00fck kareler regresyonunu kullanmakt\u0131r; bu regresyon, g\u00f6zlemlere a\u011f\u0131rl\u0131klar atayarak, d\u00fc\u015f\u00fck hata varyans\u0131na […]<\/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-1334","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"\n 1. Ad\u0131m: Verileri olu\u015fturun<\/strong><\/span><\/h3>\n
df <- data.frame(hours=c(1, 1, 2, 2, 2, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 8),\n score=c(48, 78, 72, 70, 66, 92, 93, 75, 75, 80, 95, 97, 90, 96, 99, 99))\n<\/strong><\/pre>\n
Ad\u0131m 2: Do\u011frusal Regresyon Ger\u00e7ekle\u015ftirin<\/strong><\/span><\/h3>\n
#fit simple linear regression model\n<\/span>model <- lm(score ~ hours, data = df)\n\n#view summary of model\n<\/span>summary(model)\n\nCall:\nlm(formula = score ~ hours, data = df)\n\nResiduals:\n Min 1Q Median 3Q Max \n-17,967 -5,970 -0.719 7,531 15,032 \n\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 60,467 5,128 11,791 1.17e-08 ***\nhours 5,500 1,127 4,879 0.000244 ***\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 9.224 on 14 degrees of freedom\nMultiple R-squared: 0.6296, Adjusted R-squared: 0.6032 \nF-statistic: 23.8 on 1 and 14 DF, p-value: 0.0002438\n<\/strong><\/pre>\n Ad\u0131m 3: Heteroskedasticli\u011fi test edin<\/strong><\/span><\/h3>\n
#create residual vs. fitted plot\n<\/span>plot( fitted<\/span> (model), resid<\/span> (model), xlab=' Fitted Values<\/span> ', ylab=' Residuals<\/span> ')\n\n#add a horizontal line at 0 \n<\/span>abline(0,0)<\/strong> <\/pre>\n![\"\"](\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/wls1.png\")
<\/p>\n #load lmtest package\n<\/span>library<\/span> (lmtest)\n\n#perform Breusch-Pagan test<\/span>\nbptest(model)\n\n\tstudentized Breusch-Pagan test\n\ndata: model\nBP = 3.9597, df = 1, p-value = 0.0466\n<\/strong><\/pre>\n\n
Ad\u0131m 4: A\u011f\u0131rl\u0131kl\u0131 en k\u00fc\u00e7\u00fck kareler regresyonunu ger\u00e7ekle\u015ftirin<\/strong><\/span><\/h3>\n
#define weights to use\n<\/span>wt <- 1 \/ lm( abs<\/span> (model$residuals) ~ model$fitted. values<\/span> )$fitted. values<\/span> ^2\n\n#perform weighted least squares regression\n<\/span>wls_model <- lm(score ~ hours, data = df, weights=wt)\n\n#view summary of model\n<\/span>summary(wls_model)\n\nCall:\nlm(formula = score ~ hours, data = df, weights = wt)\n\nWeighted Residuals:\n Min 1Q Median 3Q Max \n-2.0167 -0.9263 -0.2589 0.9873 1.6977 \n\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 63.9689 5.1587 12.400 6.13e-09 ***\nhours 4.7091 0.8709 5.407 9.24e-05 ***\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 1.199 on 14 degrees of freedom\nMultiple R-squared: 0.6762, Adjusted R-squared: 0.6531 \nF-statistic: 29.24 on 1 and 14 DF, p-value: 9.236e-05\n<\/strong><\/span><\/pre>\n Ek kaynaklar<\/strong><\/span><\/h3>\n
R’de \u00e7oklu do\u011frusal regresyon nas\u0131l ger\u00e7ekle\u015ftirilir<\/a>
R’de niceliksel regresyon nas\u0131l ger\u00e7ekle\u015ftirilir<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"