Let's say I am trying to estimate E(y | x1, x2....). The dataset has two subcategories, say URBAN and RURAL. The descriptive stats of the two subsets are very different, as are the coefficients from regressions run separately. For example, I can see that E(y|x1), E(y|x2) etc are all positive for URBAN and all negative for rural. In this case, is it still justified to run a pooled regression with interactions thrown in? Or, do we assume that two samples are really from two different populations and hence the models should be estimated separately? Is there any way to test (frequentist or bayesian) if the two samples came from the same underlying population?