Mary Le, you can test an interaction effect between a dummy variable (X1) and a continuous predictor (X2) using regression. You first create a product term (X3) through X1*X2. After estimating your model including X1, X2 and X3, B3-coefficient will tell you the difference between the coefficients of the two categories of your dummy variable (X1).

Dear Mehmet,

Thank you so much for your answer. As you said, we can test interaction effect between dummy variable and a continuous predictor, but can we test interaction effect of two dummy variables in the same way???

Yes, the same principle applies to testing an interaction between two dummy variables.

Thank you so much, professor Mehmet!!

You wrote:" i transform them into continuous variables by using 2 dummy variables ", that is simply wrong. You did not transform them into continous variables, they are still dichotomous, you probably just changed the coding for better interpretation. It yould be any coding, effect, Helmert...., none of them make dichotomous variables magically continous. But Mehmet is correct, you can create every interaction term you want to test.

many thanks to you, Rainer Duesing