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.
For example, if we have in one model y=a+bx while in the second model we have y*=a*+b*x* where y*=log(y) and x*=log(x), say. How would you compare the two models? If we want a regression model that is excellent both for fit and for prediction, are there specific regression diagnostics we could use here?
Thank you for your feedback, Vahab.
You are addressing which transformation to pick. I am aware of what you have stated. My question really is about regression daignostics that we get back from most regression analysis software.
Consider a regression of y on x (Model 1) and a regression model log(y/z) on x. The response variable changed from y to log(y/z). Is a comparison of MSE meaningful here?
Which other regression metrics could be used to compare Model 1 with Model 2?
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