# Interpreting coefficients in MLR model with interaction term

$\hat{IQ} = 100 + 0.1*gender + 4.3*athletic+ 0.3*gender * athletic$

This is a model with 2 binary predictors: gender (0 = female, 1 = male), athletic (0 = no, 1 = yes) and an interaction term.

$\hat{B}_0 = 100$: the expected IQ score is 100 for a female who is non-athletic.

$\hat{B}_1 = 0.1$: the expected change in IQ is 0.1 units for a male rather than a female, given that he is non-athletic.

$\hat{B}_2 = 4.3$: the expected change in IQ is 4.3 units for an athlete vs. non-athlete, given that the person is female.

Are the above interpretations correct? And now comes the tricky part with interpreting the interaction term between two categorical variables. I've looked at this post and its suggestion on rewriting the model in a different format; however, I do not see how that would help me interpret $\hat{B}_3$, the interaction coefficient.

Male athlete: 100 + 0.1 * 1 + 4.3 * 1 + 0.3 * 1 = 100+0.1+4.3+0.3 = 104.7

Without the interaction term the male athlete would have 104.4. The interaction term does only have an impact on the dependent variable for male athletes.

Male non-athlete: 100 + 0.1 *1 + 4.3 *0 + 0.3 *0 = 100 + 0.1 = 100.1

Female athlete: 100 + 0.1 *0 + 4.3 *1 + 0.3 *0 = 100 + 4.3 = 104.3

Female non-athlete: 100 + 0.1 *0 + 4.3 *0 + 0.3 *0 = 100

• Yes, I understand. But how exactly would you interpret the interaction coefficient in this context? – Adrian Sep 20 '16 at 15:45
• B1 = difference female & male non-athletes B2 = difference female non-athletes & female athletes (B1 + B3)= different male athletes and male non-athletes – Ferdi Sep 20 '16 at 16:05
• So I can't interpret just B3? I have to interpret it in terms of B1 + B3? – Adrian Sep 20 '16 at 16:09
• B3 is the difference between i) the effects of women doing sports and ii) the effects of men doing sports – Ferdi Sep 21 '16 at 7:45