COMPARISON OF LEAST MEDIAN SQUARE AND ORDINARY LEAST SQUARE METHODS IN THE PRESENCE OF OUTLIERS

Abstract

The general assumption concerned with linear regression model is that under ideal conditions the ordinary least square performs better than other regression methods. However under some non-ideal conditions, that is, when the general assumption of normality is violated the ordinary least square breaks down. Thus, this study aimed to compare the efficiency of ordinary least squares (OLS) and least median squares (LMS) estimators by subjecting both estimators to dataset with and without the presence of outliers. We made use of real and simulated data. The simulated data were obtained from R program. The data was analyzed with multiple linear regression methods (Ordinary Least Square and Least Median Squares). Also, the residual standard error of both models and the standard error of the coefficients (intercept and slope) were used to assess and compare their performances. The result of the regression analysis shows that the OLS perform better when normality of the data is not violated; however, the OLS perform poorly compared to LMS when the normality is violated due to the presence of outliers as revealed by its higher residual standard errors and parameters standard errors.