For every model of relationship between y and x
If all the observations are on the model then r^2=1
Fortunately r turns out to be normalized covariance 🙂
Adjusted R2 is
where p is the total number of regressors in the linear model (not counting the constant term), and n is the sample size.
Adjusted R2 can also be written as
where dft is the degrees of freedom n– 1 of the estimate of the population variance of the dependent variable, and dfe is the degrees of freedom n – p – 1 of the estimate of the underlying population error variance.
The principle behind the adjusted R2 statistic can be seen by rewriting the ordinary R2 as