Another Cautionary Note about R²: Its Use in Weighted Least-Squares Regression Analysis

Abstract

A recent article in this journal presented a variety of expressions for the coefficient of determination (R ²) and demonstrated that these expressions were generally not equivalent. The article discussed potential pitfalls in interpreting the R ² statistic in ordinary least-squares regression analysis. The current article extends this discussion to the case in which regression models are fit by weighted least squares and points out an additional pitfall that awaits the unwary data analyst. We show that unthinking reliance on the R ² statistic can lead to an overly optimistic interpretation of the proportion of variance accounted for in the regression. We propose a modification of the estimator and demonstrate its utility by example.

Key Words:

• Coefficient of determination
• Multiple R ²