Writes Pesaran (1974): Consider a model with $k-1$ regressors and the same model with an extra regressor. Then it can easily be seen that
$\bar{R}_{k}^{2} - \bar{R}_{k-1}^{2} = \frac{1 - \bar{R}_{k}^{2}}{n-k+1} \left( \hat{t}_{k}^{2} - 1 \right)$
where $\bar{R}_{k}^{2}$ and $\bar{R}_{k-1}^{2}$ denote the adjusted multiple correlation coefficients for the models with $k$ and $k-1$ explanatory variables respectively, and $\hat{t}_{k}$ is the estimated $t$-ratio of the added variable.
Unfortunately he does not derive this result. Does anyone know how it works?
