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?
