Comparison of Weights in Weighted Least Square Method For Handling Heteroscedasticity on Multiple Regression Model

Abstract

Regression analysis is the most popular and commonly used to determine causality between two or more variables. In regression analysis there are several assumptions that must be held, so that the property of the best linear unbiased estimator (BLUE) is still guaranteed. In fact, we often found violations of the assumptions.  One of them was violations of the homoscedasticity or occurs heteroscedasticity. The impact of heteroscedasticity in the regression model is that the ordinary least square (OLS) estimator no longer has a minimum variance although still linear and unbiased. To handle this, weighted least square (WLS) regression is used instead, which giving weights on the observations. But the problem often encountered is choosing which the best weight in WLS method. This paper aimed to compare and determine the best weight among 1/X, 1/ , 1/Y and 1/s in multiple regression model. Human development index factors data, which were obtained from the Indonesian Central Bureau of Statistics, were used. The results showed that the best weight on human development index data was 1/s.  The coefficient of determination was 98.7% indicating that the model was very good.