If we have several models as follows:
1. response variable: y regressor variable: x
2. response variable: y* regressor variable: x*
3. response variable: y** regressor variable: x**
where y* and y** are transformations of y, and where x* and x** are transformations of x.
How would you best compare such models?
The units of y and y* and y** differ from each other, so which regression statistics would you recommend to be used, and why?
Is R square meaningful here for comparing the three models for fit and for prediction capabilities?
Is the F test for the significance of the regression a useful metric here?
What about MSE?
How about using as "r square for prediction" 1-(PRESS/SS Total), say?
Should I obtain the model with slope and intercept, and then re-transform to the original units to somehow measure how good the fit really is?
Your feedback is appreciated.
Thanks.