CPANEL Procedure
R-Square
The R-square statistic is the proportion of variability in the dependent variable that is attributed to the independent variables. Because of the transformations that are used prior to fitting the final regression model, the conventional R-square measure is not appropriate for most of the models that the CPANEL procedure supports. In random-effects models that use a GLS transform, PROC CPANEL calculates the modified R-square statistic proposed by Buse (1973),
where 
is the error sum of squares from the final model fit, 
represents the GLS transform, and 
for 
.
In GLS models that do not have an intercept, the alternative R-square measure, which is attributed to Theil (1961), is calculated as follows:
In fixed-effects models, the R-square measure is
where 
is the within-transformed dependent variable.
In the case of pooled OLS estimation, all three of the R-square formulas reduce to the usual R-square statistic for linear models.
The R-square statistic is not appropriate for IV regression and dynamic panel estimation, and thus it is not reported for these models.