Suppose I have a dataset with dependent variable y, and several (round 50) features (or independent variables) x_s, and I decide (/am required) to use linear regression (ols or glm, with or without regularization). Usually I will look at the distribution of x_s and y, and transform them (such as using log) if necessary, but after reading the answer to this question:linear regression on exponential distributed dependent variable, I am a little confused weather it is useful at all. My question is that since validity of linear regression doesn't have direct link to the distribution of x_s and y, is it right/necessary thing to do to transform the variables if the distribution looks non-normal?

which leads to another general question when applying linear regression: nowadays we are dealing with high dimensional dataset everyday, which after some basic feature selections, there are still around few hundred features left, the way I deal with this dataset is that I would transform some features which are non-normal, then apply stepwise regression on all the features plus the transformed features. it there a better way to do it?

  • $\begingroup$ I think this has been discussed countless times here on the site, and for sure it's explained in the answer you link to. The marginal distributions of predictors and response don't matter: what matters is the conditional distribution of the response with respect to the predictors. $\endgroup$
    – DeltaIV
    May 12, 2017 at 7:37