Generalization of the Coefficient of Determination or R-square and its application to Self-Referencing Models

Abstract

The traditional coefficient of determination or R-square is the proportion of variation explained by a regression model versus the variation explained by the mean. This measure does not discriminate well between alternative self-referencing models such as site index curves. A generalized R-square based on the proportion of the variation explained by the self-referencing model versus the variation explained by a straight line through zero for each growth series provides better discrimination between candidate models. Three growth series from the South Africa Correlated Curve Trend Study are used to illustrate the difference between the traditional R-square and the generalized R-square.