# How do we interpret the results of regression for log transformed data containing negative values, $\log(Y-\min(Y)+1)$?

I have a question regarding interpretation of regression results based on data where I have some negative values. Since the residuals were positively skewed I needed to log-transform my data, and because of negative values my log transformation looked like $\ln(Y-\min(Y)+1)$. Normally, if we have $\ln$ in both sides of the equation, then our $b$ coefficient means a percentage change of DV for 1 % change of IV. But I have big doubts whether the same is valid for such log-transformed data, where I added a constant to my DV in order to make the minimum value equal to 1. I can't also find any literature on this topic. Does anyone know for sure what would be the correct interpretation in such a situation?

• @DimitriyV.Masterov , would the results of a glm approach with a log link function be interpreted the same way one would interpret a simple lm( log(y) ~ log(x)) ? – rafa.pereira May 7 '17 at 22:48