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A robust coefficient of determination for regression
Authors:Olivier Renaud  Maria-Pia Victoria-Feser
Institution:1. Methodology and Data Analysis, Psychology Department, University of Geneva, CH-1211 Geneva 5, Switzerland;2. Distance Learning University, CH-3960 Sierre, Switzerland;3. Faculty of Economics and Social Sciences, University of Geneva, CH-1211 Geneva 5, Switzerland
Abstract: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 practitioners. Indeed, it is reported in most statistical analyzes, and although it is not recommended as a final model selection tool, it provides an indication of the suitability of the chosen explanatory variables in predicting the response. In the classical setting, it is well known that the least-squares fit and coefficient of determination can be arbitrary and/or misleading in the presence of a single outlier. In many applied settings, the assumption of normality of the errors and the absence of outliers are difficult to establish. In these cases, robust procedures for estimation and inference in linear regression are available and provide a suitable alternative.
Keywords:Consistency  Efficiency  Outliers  R-squared  Correlation
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