A measure to identify regression outliers

Abstract

In this paper we describe a measure that can be used to detect regression outliers. Observations that deviate from the bulk of the data can easily influence the fit of the least squares regression line, and the residuals, which take the response variable,y, into account, are often examined to determine the observations that may have influenced the fit of the least squares regression line, hence affecting other regression estimates. One drawback of using transformed residuals such as the Studentized residuals is that they may fail to identify the regression outliers when these observations are being accommodated by the least squares fit, thus we propose a measure that is based on the role that each observation plays in the displacement of other observations from the fitted least squares regression line. The proposed measure is based on the off-diagonal values of the hat matrix, and illustrated on three data sets that have appeared in the literature on regression diagnostics. A comparison is also made using popular MM estimator used to obtain robust regression estimates to illustrate the value of the proposed measure.