UC Santa Barbara

Let R denote the population multiple correlation coefficient of one variable on the other (m-1), in a m-variate normal —2 distribution. Bayes estimator of R, given only the sample 2 multiple correlation coefficient R, is derived with respect to the squared error loss function and a Beta prior distribution.-2 These results are then related to the Bayes estimates of R /(1-_o R), a parameter considered recently by Muirhead (1985). The ideas are illustrated and the effect of various parameters studied through numerical examples. A Monte Carlo study indicates that the sampling mean squared error of the Bayes estimator is lower than that of R2, for plausible prior distributions. © 1989, Taylor & Francis Group, LLC. All rights reserved.