In Linear regression model, Ordinary Least Square estimate is considered the best method to estimate the parameter if all the assumptions are met. The violation of some of these assumptions may give misleading result due to the presence of outliers, hence, the need for the use of robust regression methods. The work investigated seven robust regression methods (Least Trimmed Squares estimates, Tukey Bisquare Estimator, Yohai MM Estimates, S- estimator, Least Absolute Value, Robust Weighted Least Squares Estimator and Least Winsorized Square for estimating regression parameters in the presence of outliers. Cases with two and five variables were compared. Simulation which covered data sets with 2%, and 10% outlying Contamination Rate and 20, 50, 100, 200, and 500 as sample sizes were performed using the R –Package. The Root Mean Square was used as the performance measure of accuracy for the estimators in predicting each of the parameters. The results obtained showed that the number of v