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

Indiana University

Susan Embretson Whitely

Kansas University

The sample squared multiple correlation coefficient, R², 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 – R² have been proposed. We examine the biases and mean squared errors of five adjusted estimators as well as R². General results are given for estimators linear in 1 – R², 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.

Key Words: Squared multiple correlation • correlation • adjusted estimators • shrinkage

Journal of Educational and Behavioral Statistics, Vol. 9, No. 3, 183-192 (1984)
DOI: 10.3102/10769986009003183


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