Comparison of Robust Methods for Multiple Linear Regression Models

The linear regression model is one of the most important basic statistical models widely used in data analysis in many fields, such as economics, social sciences, and medicine. This model used to illustrate the relationship between a dependent variable and several independent variables. Although the ordinary least squares (OLS) method is effective for estimation under appropriate conditions, the presence of outliers or extreme values ​​may reduce the effectiveness and accuracy of these estimates. Therefore, the need has emerged to use alternative and more robust estimation methods to address these observations, known as robust estimation methods. This study compares the classical ordinary least squares method with several robust methods, such as the S-estimation, M-estimation, MM-estimation, and Huber methods, to evaluate their performance in the presence of data contamination. The analysis results showed that the Huber method outperformed the other methods when contamination levels reached 7% or more, making it an effective choice for obtaining more accurate and reliable estimates in environments containing imperfect or contaminated data.