Estimation in Multiple Correlation/Prediction

Abstract

The distinction between the square of a population correlation coefficient (ρ²) and of the true validity of a sample prediction equation (ρ _v²) 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 ρ², R_R² (Ezekiel) and R_OP² (Olkin and Pratt), and of three estimators for ρ_v ² , R_NL² (Nicholson, Lord), R_SD² (Stein, Darlington) and R_LO ² (a jack-knife-like estimator). Interpretive approaches to, and problems in, multiple correlation/prediction estimation are discussed.