I have been trying to examine the association between two variables (y1 and x1). Y1 does not have a normal distribution and positively skewed. From other qualitative estimates, association at both extreme quantiles are different from the middle section. I have done a quantile regression. But I am unable to do further tests to establish the differences. I would appreciate your suggestions for necessary diagnostic tests. I use Stata, but I am not very competent. So I would be interested in the syntax as well (please see the attached doc for more details and coefficients).