It seems to me that smoker
is a dummy variable (1/0) [please see the note below]. Please double check the following sentence:
We run a linear regression of cholesterol level on a full factorial of age group and whether the person smokes along with a continuous body mass index (bmi) and its interaction with whether the person smokes [emphasis]
cholesterol = -0.517 smoker + 0.03455 bmi + 0.0245 bmi*smoker + other parts
The coefficient on bmi
indicates the impact of bmi
for non-smoker whereas the coefficient on bmi*smoker
gives the incremental impact of bmi
for smoker (i.e. for smoker it is 0.03455 + 0.0245 vs 0.03455 for non-smoker). The significance of the interaction term indicates that impact on cholesterol of bmi
is higher for smokers than for non-smokers.
Note: There are three categories of age group, not three categories of smokers.