I am sorry for bothering you with details of this question. I am studying turnout disparity between rural and urban areas in a developing country. My theory suggests that rural and urban areas have fundamentally different modes of participation. (I developed a hypothesis based on this theory) Currently, I have a pooled sample of turnout and several independent variables in about 700 districts. In order to test hypothesis, I think I need to split the sample between urban and rural areas. I generated a dichotomous variable of urban/rural districts. I run two regressions (one for urban and the other for rural areas), and then compared the coefficients. I run the two regressions with “suest test”. Among several independent variables, only for one regression coefficient the prob>chi2 is less than .05, and this variable is the main independent variable according to the theory. For the rest of variables (which are the controls) the the prob>chi2 is larger than .05. (the implied homoscedasticity is unacceptable for this variable, I run robust regression, and the result is almost the same).
I have a difficult time to interpret the result. If “only one” coefficient (which happens to be main independent variable) varies between rural and urban districts. Can I conclude that my hypothesis about the fundamentally different modes turnout (between urban and rural districts) is correct? OR all other control variables should interact with urban/rural variables and have the chi2 less than .05 to support my idea about the different modes of turnout?

Many thanks