The literature on three-variable multiple regression contains two major statements, (a) There is no use in adding a second predictor to a bivariate regression equation when the correlation between that predictor and the first equals unity, (b) The squared multiple correlation (R2) equals the sum of the two squared validities whenever the correlation between the predictors equals zero. In this paper we define two rules each generalizing one of these ‘rules of thumb.’ These two rules are stated and discussed in terms of the relation between the ratio of the two validities and their intercorrelation.
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