The weighted least squares ratio (WLSR) method to M-estimators

The regression analysis is a considerable statistical instrument applied in many sciences. The ordinary least squares is a conventional method used by Regression Analysis. In regression analysis, the least squares ratio method outperforms than the ordinary least squares method, especially in case of the presence of outliers. This paper includes a novel approach to M-estimators, named the weighted least squares ratio. The aim of this study is to determine which method gives better result in case of increasing outlier and variance while establishing a regression model. The weighted least squares and the weighted least squares ratio methods are compared according to statistics values of mean absolute errors of estimated the regression parameters and dependent value.