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The Biases And Mean Squared Errors Of Estimators Of Multinormal Squared Multiple Correlation, Joseph F. Lucke, Susan E. Embretson

Joseph Lucke

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.