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Precision of Prediction NICHD

Browne, Michael W.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
National Institute for Child Health and Human Development (NICHD), Error of Measurement, Mathematical Formulas, Models, Multiple Regression Analysis, Prediction, Statistical Analysis


Precision of prediction in multiple linear regression is examined. Two measures of predictive precision, predictive mean square error, d2, and the squared weight validity, w2, are employed. The use of an existing estimator of E{d2} as an estimator of d2 is proposed and the mean squared error of estimation of this estimator about d2 is obtained. A significance test is given. Estimators of w2 are derived and an asymptotic approximation for their variances is given. These estimators of w2 are functions of estimators of p2, the squared multiple correlation coefficient, and of p4. The bias and mean squared error of estimation of some known estimators of p2 and of a proposed estimator of p4 are examined. Monte Carlo experiments are used to compare the proposed estimators of w2 with an estimator due to Burket 1964 . An efficient procedure for generating w2 and the estimates of w2 is described. The mean squared errors of estimation of cross-validation estimators of d2 and w2 are obtained and disadvantages of the cross-validation procedure are discussed. An example is used to illustrate relationships between predictive precision and the number of predictors. The paper is primarily concerned with a random predictor model but results for a fixed predictor model are also given.

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