infonet-economy

To assess the quality of the fit in a multiple linear regression, the coefficient of determination or R2 is a very simple tool, yet the most used by statistics users. It is well known that the classical (least-squares) fit and coefficient of determination can be arbitrary misleading in the presence of a single outlier. In many applied setting, the assumption of normality of the error and of absence of outliers are difficult to establish. In these cases, robust procedures for the estimation and the inference in linear regression are available and provide an excellent alternative. In this paper we present a companion robust coefficient of determination that has several desirable properties not shared by others: it is robust to deviations from the specified regression model (like in the presence of outliers), it is efficient if the errors are perfectly normal, and we show that it is a consistent estimator of the population coefficient of determination. A simulation study and two real datasets support the appropriateness of this estimator, compared with classical (least-squares) and existing robust R2.