Question

1. In the following regression, “drink” is a dummy indicating a person drinks alcohol, “smoke” is a dummy indicating a person smokes cigarettes, and “drink*smoke” is the interaction of the two variables:

Medical Bill=1+2 drink+3 smoke+4 drink*smoke+other

1. How much is the difference in medical bill between a person who both drinks and smokes and a person who doesn’t drink but smokes?  

2. Will you be able to test if this difference is statistically significant if you are given all the standard errors? Say “yes” or ‘no”, then explain.  

Answer 1

The independent variable drink*smoke will take value of 1 for one who both somkes and drinks and all the other independent variables will take a value of 0 for this person, and so on.

Hence the amount of medical bill is higher by the coefficient of drink*smoke for this person as compared to someone who neither smokes nor drinks. Similarly the amount of medical bill is higher by the coefficient of smoke for one who only smokes as compared to who does neither smoke nor drink.

Hence the difference between the coefficients of drink*smoke and of smoke represents the difference between their medical bills.

Given that the 4 variables (smoke, drink, smoke*drink, neither (which need not be written separately, and the absence of all of them would mean the presence of this one) are MECE, it should be possible to test for their statistical significance.