How to interpret the beta estimates of a generalized linear model with a square root power link?

Cross Validated Asked by StatBoy_41 on December 10, 2020

I’m running a generalized linear model (GLM) in SAS with a gamma distribution (since my Y response variable is skewed to the right) and a specified square root power link (since I found that transforming my Y via the square root improves the skewed distribution). I have 2 X predictor variables, X1 and X2.

Using the PROC GENMOD procedure, SAS gives me an output of the 2 regression estimates for X1 & X2. For example:

X1: 0.64

X2: -0.08

How would I go about interpreting these estimates in terms of my Y variable? Do I have to take the square of the estimates to obtain the original un-transformed Y?

i.e. 1 unit change in X1 yields a (0.64)^2 change in Y

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