# interpreting coefficients of interaction terms between categorical variables [closed]

Assuming I have a linear regression model of the form:

Y = a + (b1*fact1) + (b2*fact2) + b3*(fact1*fact2) + b4*other_var

where, fact1, fact2 are categorical variables of 2 factors each, YES and NO and other_var is a continuous variable and in the regression model, b3 represents the coefficient when both fact1=fact2=YES

a) is the intercept a, the effect on response Y in the case where both fact1 and fact2 are 0?

b) is the effect on the response Y when fact1=fact2=YES, given by b1+b2+b3?

c) is the effect on the response Y when fact1=YES, fact2=NO, given just by b1?

Model structure as shown in the picture for easier reference:

## closed as off-topic by COOLSerdash, Peter Flom♦Mar 11 at 11:37

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• If this is related to a school/college assignment, please add the self-study tag, and show us what you've been able to do, so we know you at least tried solving the problem. – Lucas Farias Mar 11 at 5:06
• the question is based on a regression output that I worked on for an assignment with a lot more variables; showing what I worked on/the output would mean taking a screenshot of the output. I'm just trying to understand if my inference is right, especially with regards to the intercept – red4life93 Mar 11 at 6:16
• @LucasFarias He came up with the right answer himself, and it is posted on the question, so it is hard to believe that he did not try – David Mar 11 at 7:19
• Possible duplicate of Does it make sense to interact 2 dummy variables? – COOLSerdash Mar 11 at 7:22

You are absolutelly right, it is exactly as you posted it (assuming other_var is equal to 0, otherwise you will have to add $$b_4 * othervar$$)