I try to do a linear regression of a positive continuous dependent variable (outcome) with several independent variables (all of them are categorical / binary). I had many troubles to get Gaussian residuals (the distribution of my outcome variable is not Gaussian itself).
I tried a lot of transformations for the outcome: log, square root, inverse... and the best one is Box-Cox with a parameter: $\lambda = -3$. The regression is correct, the residuals are Gaussian, and homoscedastic. But I have found the Box-Cox is not the easiest thing to interpret. The original outcome represent a delay and there is no way to interpret the transformed outcome with a mix of power and inverse. And when I want to come back to my original outcome, I have cube root (or power 1/3).
My questions are:
- How is the change of a given binary variable modality on my original outcome, knowing the corresponding coefficient?
- Can I do the same thing with the confidence interval (2.5% and 97.5% limits) of the regression coefficients?