Filtering and Denoising in Linear Regression Analysis

In this paper we examine the effect of outlier/leverage point on the accuracy measures in the linear regression models. We use the coefficient of determination, which is a measure of model adequacy, to compare the effect of filtering approach on the least squares estimates. We also compare the performance of the filter-based approach with several resistant methods in a situation where there are several outliers in the data sets. Specifically, we examine the sensitivity of the resistant methods and the proposed approach in the circumstances where there are several leverage points in the data sets. To gain a better understanding of the effect of filtering and evaluating the performance of the proposed approach, we consider real data and simulation studies with several sample sizes, different percentage of outliers, and various noise levels.