Just a question on regression model evaluation statistics. Here we go.
I seem to be under the impression that $R^2$, MSE, and RMSE are all very closely related and essentially all play a part in determining the fit of a model, but somehow I am still confused about which one, then, I should be using as a final determinant of how good/bad my model is performing, or how is it that I can consider all three as separate indicators (with them being so similar)?
It just seems like no matter what, the model with the $R^2$ closest to 1 also has the lowest MSE and RMSE values. I read that "sometimes" the $R^2$ doesn't determine the fit properly, and so the other metrics should be the determinants of fit, but if they all correlate (one goes up, the other goes up, and vice versa), is there even reason to separately consider them? (<- my bad if this seems redundant)
That's all I've got. Thanks for your time!