# Testing for the significance of the difference-in-differences of adj. R²

Is there a way to test for the significance of the difference-in-differences in adj. R²s in Stata?

Let's say I have four subgroups: pre-treatment, pre-control, post-treatment, post-control and I want to figure out whether the difference-in-differences of the adj. R² of the same regression (e.g., R² of Y = b0 + b1*X + e) conducted for each of the four subgroups is signficant.

I read somewhere that it might be possible to bootstrap the adj. R² of each regression and then test for the difference-in-differences, but I am not sure if this would be an appropriate approach?

Thanks a lot!

Whilst it is true that you can bootstrap $\text{R}^2$ and $\overline{\text{R}}^2$ (see Ohtani (2001) "Bootstrapping $\text{R}^2$ and adjusted $\text{R}^2$ in regression analysis") the procedure you propose will result in having 4 numbers, i.e. the four $\text{R}^2$ or $\overline{\text{R}}^2$ from the regressions of $Y$ on $X$ for the treatment and control groups in the two time periods. In this case you end up like the OP of this earlier question who tried to achieve exactly that but finally figured out that it could not be done. So even if you can construct a standard error or confidence interval for each coefficient of determination itself, with four numbers there is no degree of freedom left in order to calculate a standard error for the difference in differences.