(See also
R ^{2}.) R^{2} adjusted for loss in the degrees of freedom. R^{2} is penalized by adjusting for the number of parameters in the model compared to the number of observations. At least three methods have been proposed for calculating adjusted R^{2}: Wherry’s formula [1(1R^{2})·(n1)/(nv)], McNemar’s formula [1(1R^{2})·(n1)/(nv1)], and Lord’s formula [1(1R^{2})(n+v1)/(nv1)]. Uhl and Eisenberg (1970) concluded that Lord’s formula is most effective of these for estimating shrinkage. The adjusted R^{2} is always preferred to R^{2} when calibration data are being examined because of the need to protect against spurious relationships. According to Uhl and Eisenberg, some analysts recommend that the adjustment include all variables considered in the analysis. Thus, if an analyst used ten explanatory variables but kept only three, R^{2} should be adjusted for ten variables. This might encourage analysts to do a priori analysis.

Uhl, N. & T. Eisenberg (1970), “Predicting shrinkage
in the multiple correlation coefficient,” Educational and Psychological
Measurement, 30, 487489.