On the determination coefficient in robust regression

In simple linear regression the determination coefficient tells us which percentage of the variance of the response variable is explained by the fitted linear mapping of the explanatory variable. In this paper we examine how to extend the notion of determination coefficient to mean absolute value and least median of squares regression. The concept behind our proposals for the extension originated in an economical context. After dealing with questions of unbiasedness and limiting behaviour for different scales of error variances we discuss a simple example with different distribution assumptions for the residuals and find that the results meet intuition. AMS SUBJECT CLASSIFICATION: 62G35; 62J05.