The full F-stat is indeed a goodness-of-fit measure for the regression model.
> I wonder if I could average these F-values across the whole brain. Would that
> make statistical sense? Would it not be better to average the R squares?
Averaging the full F-stat across the brain is probably not a good idea because F-stat is a nonlinear measure, and resulting average value is difficult to interpret. And yes R^2 is a better candidate for that purpose.
Gang