This paper is concerned with introducing the most used penalized regression methods, including ridge regression (RR), least absolute shrinkage and selection operator (LASSO), and elastic net (EN) regression for estimating the linear regression model. These models are used in two cases low and high-dimensional data when data iscontain outliers when the explanatory variables have collinearity among them. The Monte Carlo simulation study is conducted to evaluate and compare the performance of these estimators. The simulation results indicate that the obtained estimators using EN are efficient and reliable than the other estimators.