Effects of a single outlier on the coefficient of determination: An empirical study

Abstract

This article investigates the effects of outliers on the coefficient of determination, R 2 which is computed by Ordinary Least Squares (OLS) estimator. It is now evident that the OLS is greatly affected by outliers and hence the R 2 is also affected. This problem can be solved by using the robust estimators such as Least Trimmed Squares (LTS) estimator. In this article, we compare the value of R 2 which is computed by OLS and LTS estimators. We modify a regression data set to effectively generate outliers in both X and Y directions. Then the coefficient of determination (OLS and LTS) is investigated from the modified data sets (data with outliers). The numerical results show the merit of using the LTS based R 2 estimator compared to the OLS estimator.