18 August 2017 4 358 Report

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.

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