The Biases and Mean Squared Errors of Estimators of Multinormal Squared Multiple Correlation

Abstract

The sample squared multiple correlation coefficient, R ², is known to have certain unsatisfactory properties as an estimator of the population squared multiple correlation. Hence, numerous adjusted estimators based on functions of 1 – R ² have been proposed. We examine the biases and mean squared errors of five adjusted estimators as well as R ². General results are given for estimators linear in 1 – R ², and four such estimators are examined in detail. In addition, a quadratic estimator and the minimum variance unbiased estimator are examined. Comparisons among these estimators are made in terms of absolute bias and mean squared error.