The Reliability of Estimated Beta Weights in Multiple Regression Studies

The reliability of beta weights estimated through the multiple regression procedure is defined as the ratio of the variance of the true beta weights to the expected variance of the estimated beta weights. Equivalently, reliability is (approximately) the expected correlation between sets of beta weights estimated from two independent data sets, each with the same number of observations. A formula for estimating the reliability of estimated beta weights in a multiple regression study is given. The relationship of reliability to sample size, number of predictors, population coefficient of determination and average predictor intercorrelation is derived. The results, although derived for the “fixed” (i.e., nonrandom) predictor case, also provide good approximations to the random predictor case.