I would like to compare the goodness of fit for a regression model fitted to two separate groups (patients and controls).
I want to compare goodness of fit (as opposed to difference in slope). I thought one way of doing this would be comparing the R value of the model in patients vs the value in controls in a Fisher R-to-z comparison.
My question is whether it is more appropriate to use the 'Multiple R-squared' or the 'Adjusted R-squared'. Additionally if the Adjusted R squared is preferred then how would one deal with negative values?
Or please do let me know if the whole approach is wrong headed