Estimating R-2 shrinkage in multiple regression: A comparison of differentanalytical methods

The effectiveness of various analytical formulas for estimating R-2 shrinka ge in multiple regression analysis was investigated. Two categories of form ulas were identified: estimators of the squared population multiple correla tion coefficient (p(2)) and those of the squared population cross-validity coefficient (p(c)(2)). The authors conducted a Monte Carlo experiment to in vestigate the effectiveness of the analytical formulas for estimating R-2 s hrinkage, with 4 fully crossed factors (squared population multiple correla tion coefficient, number of predictors, sample size, and degree of multicol linearity) and 500 replications in each cell. The results indicated that th e most widely used Wherry formula tin both SAD: and SPSS) is probably not t he most effective analytical formula for estimating p(2). Instead, the Prat t formula and the Browne formula outperformed other analytical formulas in estimating p(2) and p(c)(2), respectively.