Perbandingan Metode Weighted Least Squares

Abstract

In multiple linear regression analysis using the Ordinary Least Squares (OLS) method as the parameter estimator, that the resulting regression coefficient estimthere are assumptions that must be met so ates are Best Linear Unbiased Estimator (BLUE). One of the violations if the assumption is not met is called heteroscedasticity where the residual variance is not constant, resulting in an inefficient estimate so that a way is needed to overcome heteroscedasticity. This study aims to compare two methods that can be used to overcome heteroscedasticity problems, namely Weighted Least Squares (WLS) and Huber-White. Using real estate dataset in Taiwan in 2012-2013, heteroscedasticity is detected by Glejser test. The application of the methods produced the following regression estimates for the OLS method OLS Y ̂= -4945,595-0,2689X_1-0,0043X_2+1,1630X_3+237,7672X_4-7,8055X_5 for the WLS method, Y ̂=1492.255-0.277X_1- 0.0079X_2+1.0197X_3+〖143.62X〗_4-〖41.396X〗_5 and for the Huber-White method, Y ̂= -4945.5951-0.2689X_1-0.0043X_2+1.163X_3+237.767X_4-〖7.8055X〗_5. These results indicate that the Huber-White method produces regression coefficients identical to those from OLS because it only corrects the standard errors. In contrast, the WLS method yields different regression coefficients since it accounts for data weights. The two methods were compared in terms of estimation efficiency. The results show that WLS is more efficient than OLS in addressing heteroskedasticity in this dataset, with an efficiency value of eff(β ̂_WLS/β ̂_OLS )<1 of 0.28 and eff(β ̂_HW/β ̂_WLS )>1 of 2.83.