Dear all
I have a problem. Now I want to examine how the variable z affects the relationship between x and y. So I conduct the regression of x on y in two groups which are grouped by the variable z（For instant，it is a dummy variable and measures ownership of a firm. It equals one if the firm is controlled by the state, and zero if the firm is controlled by a private owner. ）.
As a result, in one group with state-owned firms, the coefficient of the variable x is significant，but in the other group with private-owned firms, the coefficient of the variable x is not significant. Can I draw a conclusion that the impact of x on y is much greater for state-owned firms than private-owned firms?
My classmate told me that I should conduct a further difference test between the two groups, such as chow test. Is that true? Should I adopt my classmate's suggestion？

Best wish
lee jack