Discriminating Between Ordinary Least Squares Estimation Method and Some Robust Estimation Regression Methods

Abstract

The lack of certain assumptions is common in ordinary least squares regression models whenever there is/are outliers and high leverage in the observations with an extreme value on a predictor variable. This could have a great effect on the estimate of regression coefficients. However, this research investigates the performance of the ordinary least squares estimator method and some robust regression methods which include: M-Huber, M-Bisquare, MM, and M-Hampel estimator methods. This study applies both methods to a secondary data set with 28 years (from 1900 to 2021) 200 meter races Summer Olympic Games with a response variable (sprint time) and three predictor variables (age, weight, and height) for illustration. Also, linearity, homoscedasticity, independence, and normality assumptions based on diagnostics regression like residual, normal Q-Q, scale-location, and cook’s distance were checked. Then, the results obtained show that the robust regression methods are more efficient than the ordinary least square estimator method.