Cautionary Note about R 2

The coefficient of determination (R ²) is perhaps the single most extensively used measure of goodness of fit for regression models. It is also widely misused. The primary source of the problem is that except for linear models with an intercept term, the several alternative R ² statistics are not generally equivalent. This article discusses various considerations and potential pitfalls in using the R ²'s. Specific points are exemplified by means of empirical data. A new resistant statistic is also introduced.