# How to calculate percent deviance explained on square-root-transformed dependent variable?

I have a multiple linear regression model with a square-root transformed dependent variable.

I want to report % deviance explained for each parameter. I assume I need to back-transform in some way, but I am not sure how. Or is it okay to report % deviance explained on the original (non-transformed) model?

I am using R to calculate model deviance, if it matters. I appreciate any insight on this issue.

• You mention deviance. It sounds like you're fitting a GLM. Why transform? – Glen_b Jan 1 '15 at 4:00

The % deviance explained is calculated by comparing the predictions (fit\$fitted.values in R) for Y to actual values of Y. It does not take into account any transformations on the explanatory variables. You might need to take into account the fact that you tested a raft of transformations when doing inference. With each transformation you are implicitly increasing the number of degrees of freedom for your numerator. R will report an adjusted R^2 but to be true to your modeling process you might need to recalculate it.