Hi.

I’m wondering if there is any regression methods that can test the interaction effect of two categorical variables on a continuous dependent variable y.

For example, Age ~ Marital_status*Degree.

# Any regression methods testing the interaction effect of two categorical variables on a continuous y

That is a very standard interaction tests. All kind of interaction assessments are possible, for all combinations of discrete/continuous X and Y variables.

If you’re dealing with multi-category categorical variables (as opposed to binary), you can use a likelihood ratio test to compare the model with the interaction terms vs. the model without the interaction terms.