Comparison between classical and robust methods for linear model parameters in the presence of outlier’s values

The subject of regression is one of the subjects that has become widely applied by those interested in various social and economic sciences, because it describes the relationship between variables in the form of an equation. The linear equation that includes explanatory variables is called the linear regression equation. To describe any phenomenon using regression models, the model assumptions must be met, as well as the importance of the accuracy of the data and its analysis on the accuracy of the results to be achieved in any scientific research. Hence, the interest in studying the integrity of the data, which is considered a necessary issue for the integrity of the results. It is obvious in any scientific research that we purify the data from outliers, if any, and then the presence of outliers in the selected sample helps to shade the results of the statistical analysis, and certainly the shading is greater the greater the number of those values or the greater the deviation of these values from the rest of the observations of the selected sample. The importance of this research came in estimating the parameters of the regression model using the usual methods (least squares) and robust methods (M method and MM method). The methods were compared using the root mean square error criterion using the simulation method, where different sample sizes were generated with four different ratios of outlier’s values. It was noted that the superiority of robust methods was observed for all ratios of outlier’s values and sample sizes.