Regression analysis is used to model the data statistically. However, data modeling and interpretation are affected by outliers and significant points. Robust regression analysis offers an alternative. In this study, the parameters that define the linear regression problem are estimated using a robust approach. The concept of shrinkage, which has been investigated for outlier detection in multivariate data. A comprehensive simulation analysis is performed to examine the breakdown value of the regression estimator, the affine equivariance, the robustness against contamination, and the efficiency with normal errors. The advantages of the suggested robust estimator in regression are demonstrated by the simulation results and real-world data examples. Simulation and research are conducted using the R software.