Model Comparisons and <i>R</i> ²

Abstract

Abstract Much of the confusion surrounding interpretation and application of the coefficient of determination, R 2, can be alleviated if it is defined explicitly as a comparison of a given model to the null model EY = β0. The model-comparison definition allows R 2 to be easily generalized, and standard extensions such as coefficients of partial determination are seen to be special cases of this generalization. Formulas become simpler, more unified, and more easily understood. Commonly cited problem areas such as R 2 for the no-intercept model and model comparisons using different values of R 2 are also clarified by this perspective.