the difficulty in estimating some of the parameters makes me wary of applying it as is.
I agree that these expected-value estimates shouldn’t be taken (even somewhat) literally. But I think toy models like this one can still be important for checking the internal consistency of one’s reasoning. That is: if you can create a model that says X, this doesn’t mean you should treat X as true; but if you can’t create a reasonable model that says X, this is pretty strong evidence that X isn’t true.
In this case, the utility would be in allowing you to inspect the sometimes-unintuitive interplay between your guesses at an estimate’s R^2, the distributional parameters, and the amount of regression. While you shouldn’t plug in guesses at the parameters and expect the result to be correct, you can still use such a model to constrain the parameter space you want to think about.
I agree that these expected-value estimates shouldn’t be taken (even somewhat) literally. But I think toy models like this one can still be important for checking the internal consistency of one’s reasoning. That is: if you can create a model that says X, this doesn’t mean you should treat X as true; but if you can’t create a reasonable model that says X, this is pretty strong evidence that X isn’t true.
In this case, the utility would be in allowing you to inspect the sometimes-unintuitive interplay between your guesses at an estimate’s R^2, the distributional parameters, and the amount of regression. While you shouldn’t plug in guesses at the parameters and expect the result to be correct, you can still use such a model to constrain the parameter space you want to think about.