Abstract
where the sum of squares are derived from the standard analysis of variance. It is well known that R2 is misleading when used to compare the fit of regressions involving different numbers of predictors. The regression sum of squares cannot decrease when new predictors are added to the equation, so that increasing the number of predictors will usually increase R2 even when the true values of the new regression coefficients are zero. In a recent article, Draper (1984) shows that R2 is normally reduced when new replicate values of y are introduced at existing values of x. The situation is clear in terms of the analysis of variance. Suppose we fit the relationship y = X,B with k predictors plus a constant term. Given m x-values with p replicates at each, we get
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