I have a question with respect to running multiple linear regressions for the entire sample and different subsamples:
I have a dataset that includes a dependent variable y and several explanatory variables x1, ..., xN and z. I am interested particularly in the binary explanatory variable z. If I split the entire dataset according to this variable z, I obtain significantly different values of the mean of y for the subsamples conditioning on z = 0 and z = 1.
Now, I would like to run 3 regressions of y on all of x1, x2, ..., xN, and (potentially) z. The first regression is for the entire sample, the second regression for z = 0, and the third regression for z = 1. Should I include z as regressor in the first regression if I would like to compare all 3 regressions or should I omit it to have the same regressors for all three regressions?