Efficiency of OLS and Huber M estimator in case of Outliers

Regression analysis is a valuable tool when dealing with real-world datasets that include several types of variables. Assumption fulfillment leads to applying ordinary least square regression (OLS) on the chosen variables. When analyzing data using traditional multiple regression, the optimal technique is the ordinary least squares (OLS) estimate, provided the requirements for regression weights are satisfied. Results and estimates from samples might be misleading if the data does not match all these assumptions. Particularly problematic for least squares regression is the presence of outliers. Robust regression analysis is a typically used method. In outliers, the research aims to compare M-estimators with OLS Estimators. The effectiveness is evaluated by comparing the Huber M estimate's coefficient with the OLS estimators. To achieve the study's objective, we use Microsoft Excel to build a Monte Carlo simulation for the response and explanatory variables, which are typically distributed. The normal distribution is used to create 1,000 randomly selected integers. In order to assess the effectiveness of the estimations, outliers with varying percentages are subsequently inserted. The results demonstrate that OLS was affected by the x- and y-axis outliers. There will be no impact on the Huber M estimate from the x-axis outliers. Outliers in the Y-direction impacted the Huber M findings.