On the Detection of Influential Outliers in Linear Regression Analysis

Abstract

In this paper, we propose a measure for detecting influential outliers in linear regression analysis. The performance of the proposed method, called the Coefficient of Determination Ratio (CDR), is then compared with some standard measures of influence, namely: Cook's distance, studentised deleted residuals, leverage values, covariance ratio, and difference in fits standardized. Two existing datasets, one artificial and one real, are employed for the comparison and to illustrate the efficiency of the proposed measure. It is observed that the proposed measure appears more responsive to detecting influential outliers in both simple and multiple linear regression analyses. The CDR thus provides a useful alternative to existing methods for detecting outliers in structured datasets.