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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.
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.
