Comparison of Ordinary Least Square (OLS) with Two-Step Robust Weight Least Square (TSRWLS) in Estimating the Parameters of the Multiple Linear Regression Model with Heteroscedastic and Outliers in the Response Variable

Abstract

The main objective of this research is to use some methods to estimate the parameters of the multiple linear regression model. The first method is the classical method, the method of ordinary least square (OLS) and the second method is the Two-Step Robust Weighted Least Squares (TSRWLS). To show the effect of each of them in estimating the parameters in light of the problem of heterogeneity of error variance and the appearance of anomalies in the data that suffer from these two problems together. This was done using Monte Carlo simulation and through the Mean Absolute Percentage Error (MAPE) comparison parameter, and applied it to real data in the field of water hardness taken from the Municipality of Baghdad-Baghdad Water Directorate-Department of Quality Control on 2019. It has been found that the Two-Step Robust Weighted Least Squares method is best method for addressing the problem of heterogeneity of error variance without being affected by anomalies values.