Question

Assume you are building an interaction model with two qualitative variable. The first variables has 3 levels. The second variable has 4 level. In total how many dummy variables do you need and how many interaction terms do you need?

Options:

a. 7 dummy variables and 25 interaction terms.

	b. 6 dummy variables and 12 interaction terms.
	C. 5 dummy variables and 6 interaction terms.
	D. 5 dummy variables and 25 interaction terms.

Answer 1

Since there are 3 levels for the first variable, we will need 2 dummy variables, since one level will be considered the baseline. Also, since there are 4 levels for the second variable, we will need 3 dummy variables, since one level will be considered the baseline. Hence, total no. of dummy variables = 5.
The interaction terms involving the levels of the two variables are: (level 1 of first variable, level 2 of second variable), (level 1 of first variable, level 3 of second variable), (level 1 of first variable, level 4 of second variable), (level 2 of first variable, level 3 of second variable), (level 2 of first variable, level 4 of second variable) and (level 3 of first variable, level 4 of second variable).

Hence, 5 dummy variables and 6 interaction terms.