Estimation in Multiple Correlation/Prediction

Abstract

The distinction between the square of a population correlation coefficient (ρ 2 ) and of the true validity of a sample prediction equation (ρ v 2 ) as the parameters of interest in multiple correlation and in multiple prediction studies, respectively, is discussed. Real data are used to illustrate the comparison of two estimators for ρ 2 , R R 2 (Ezekiel) and R OP 2 (Olkin and Pratt), and of three estimators for ρ v 2 , R NL 2 (Nicholson, Lord), R SD 2 (Stein, Darlington) and R LO 2 (a jack-knife-like estimator). Interpretive approaches to, and problems in, multiple correlation/prediction estimation are discussed.

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