How to deal with significant interaction in multiple regression

[Neha Dewan]

Dear all
I apologize for posting the same question earlier in sandbox and just realized sandbox might not the right place to post.

I am doing multiple regression analysis using stata 12. While regressing using command regress Y X, the independent variable (X) explains 15% of variability in dependent variable(Y). But, interaction is highly significant between my continuous independent variable and gender(0 male,1 female). If I include gender along with independent variable in my model using command (regress Y X gender) R2 increases by another 3% and including interaction term using command (regress Y c.X##i.gender) results in R2=25%. As per my understanding, if interaction is not significant, I can remove it and and can come to final model or I can even use ANCOVA to determine if gender is acting as covariate or confounder and can present unadjusted and adjusted means accordingly. But, I am not sure how can I go ahead with SIGNIFICANT INTERACTION in multiple regression.
I will be thankful if you kindly suggest me whether I should include gender x independent variable (x) interactions in my final model or How exactly I should go ahead to come to my final model using multiple regression or suggest me some resource where I could find similar information?

Thanking you for your time
Regards
Neha

[Clyde Schechter]

A significant gender#X interaction tells you that the Y-X relationship among males is different from the Y-X relationship among females. Unless this difference is a reflection of the effects of some other variable(s) that you can include in the model, you need to keep the gender#X interaction in the model. Without it, your model is mis-specified and your coefficient of X is an attempt to estimate a non-existent parameter. I should point out that not only is your gender#X interaction term statistically significant, you tell us that it explains 10% of the variance in Y when added last: that's a lot. So the omission would probably be much more than just a minor technical problem.

To get a good file for it, try picking some representative values of X, and doing

margins gender, at(X=(list of representative values of X))
marginsplot

That will show you how different the X-Y relationship is by gender.

[Neha Dewan]

Thanks for your suggestion Clyde. I have just used margins gender after my regress command and it does tell me difference in XY relationship with gender. Thanks for your time.
Regards
Neha