Transforming skewed distribution of dependent variable in linear regression? As I understand it, the skewness of the response variable in a linear regression does not need to be normal (only the residuals need to be normally distributed). However, I was generally wondering if I can log-transform my response variable so its distribution becomes more normal prior to regression and if this has any benefits/drawbacks.
For context, my response variable y is Medicaid coverage, which has a right-skew in the state I am analyzing. If I log transform this variable using np.log(y + 1), the distribution looks approximately normal. I was wondering if this would be appropriate for a linear regression, or if I don't even need to do this/it is bad practice to do this.

In classical regression, there are no normality assumptions about the distribution of predictors in the regression or even the response (Y). All assumptions are based on residuals. It is assumed that the residuals should be approximately normal. Transforming the predictors or outcome might alter the distribution of residuals. Look for the influential observations using Cook's distance to see if any of your extreme values have high influence. Transformations are good whenever u have a meaningful interpretation, for instance, the log transform and reciprocal are often useful depending on context.
