Evaluating the predictive power of regression models

Abstract

Regression models are routinely developed and used in aquatic sciences for predictive purposes. Although the traditional measures of predictive power for regression models (r2, root mean square error) have well- defined statistical meanings, they do not necessarily provide an intuitive measure of the predictive utility of regression equations. It is proposed that an index of predictive power can be developed on the basis of the degree of categorical resolution a regression model can achieve. This index of resolution power is shown to increase nonlinearly with the familiar r2 statistic, even under different distributional assumptions. This relationship also shows that the predictive power of models with r2 ≤ 0.65 is low and nearly constant but increases very rapidly for higher r2 values, thereby justifying the search for additional explanatory variables even in models already explaining a large fraction of the variation.