The forward regression tries one by one the variables using the F-test, basically partial F-test every time for the latest variable. This is the same as testing the significance of the coefficient of this latest enetered variable. Alternatively the correlation can be used and this case the partial correlation coefficient. There is a direct relationship between the t-test statistic and the partial correlation coefficient. Now, instead of having to calculate the test statistic, we calculate the partial correlation coefficient. Using Fisher's z-transform we get the variance imediately. The partial correlation coefficient, using Fisher's z-transform, and the partial F-test (or the coefficient's t-test statistic) are not identical. They will be identical for large sample sizes though.
Authors: Michail Tsagris and Manos Papadakis