Assumptions in the classical linear regression model include that of lack of autocorrelation of the error terms and the zero covariance between the explanatory variable and the error terms. This study is channeled towards the estimation of the parameters of the linear models for both time series and cross-sectional data when the above two assumptions are violated. The study used the Monte-Carlo simulation method to investigate the performance of six estimators: ordinary least square (OLS), Prais-Winsten (PW), Cochrane-Orcutt (CC), Maximum Likelihood (MLE), Restricted Maximum- Likelihood (RMLE) and the Weighted Least Square (WLS) in estimating the parameters of a single linear model in which the explanatory variable is also correlated with the autoregressive error terms. Using the models’ finite properties(mean square error) to measure the estimators’ performance, the results shows that OLS should be preferred when autocorrelation level is relatively mild (ρ = 0.3) and the PW, CC, RMLE, and MLE estimator will perform better with the presence of any level of AR (1) disturbance between 0.4 to 0.8 level, while WLS shows better performance at 0.9 level of autocorrelation and above. The study thus recommended the application of the various estimators considered to real-life data to affirm the results of this simulation study.