st: Comparing regression fits of 2 different DVs to the same IV

[Jared Saletin <jsaletin@berkeley.edu>]

Hi all,

I was hoping to ask for a little sage stat wisdom from the list.

I have two different behavioral metrics (Y1 and Y2), and I'd like to regress each onto the same within-subject predictor (X).

I've created two models:

Y1 = B0 + B1X1;

Y2 = B0 + B1X1; 

Given that Y1 and Y2 are related but different aspects of a behavioral task, I'd like to examine whether X1 has a different predictiveness on Y1 than on Y2. I know there are tests for comparing overlapping correlation coefficients, however I'd like to be able to do it within the realm of regression. Does anyone one know if this is possible?

It seems that options would included comparing standardized regression coefficients or r-squares, but it doesn't seem like either scenario is correct in a case where the DV's differ, but the IV's are the same. 

Any help would be greatly appreciated!

Cheers,
Jared.
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