Question

In the following regression, “drink” is a dummy indicating a person drinks alcohol, “nodrink” is a...

  1. In the following regression, “drink” is a dummy indicating a person drinks alcohol, “nodrink” is a dummy indicating a person does not drink alcohol, “smoke” is a dummy indicating a person smokes cigarettes, and “nosmoke” is a dummy indicating a person does not smoke cigarettes:

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

            * indicates interaction of two variables.

  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?   

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.  

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Answer #1

Yes, if there are a large enough number of observations, it is possible to test if the difference is statistically significant. What essentially we are saying is that the population is divided into 4 categories:

Drink + Smoke

Drink + Non-smoke

Non-drink + Smoke

Non-drink + Non-smoke

All of these are MECE (mutually exclusive and collectively exhaustive) and we should be able to find out if the instance of medical bill is statiscally different for each of the categories.

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