In this study, Leverage Based Near Neighbour–Robust Weighted Least Squares (LBNN-RWLS) method is proposed in order to estimate the standard error accurately in the presence of heteroscedastic errors and outliers in multiple linear regression. The data sets used in this study are simulated through monte carlo simulation. The data sets contain heteroscedastic errors and different percentages of outliers with different sample sizes. The study discovered that LBNN-RWLS is able to produce smaller standard errors compared to Ordinary Least Squares (OLS), Least Trimmed of Squares (LTS) and Weighted Least Squares (WLS). This shows that LBNN-RWLS can estimate the standard error accurately even when heteroscedastic errors and outliers are present in the data sets.