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

a) 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? (10pts)

b) 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. (10pts)

2. In the following regression, “drive” is a dummy indicating a person owns a personal vehicle, “employed” is a dummy indicating a person is employed, “age” is a person’s age, and “married” is a dummy indicating a person is married:

drive=0.3+0.2 employed+0.003 age+0.4 married

The command in STATA is: reg drive employed age married

a) Interpret the coefficient 0.2 on employed. (10pts)

b) Predict the probability of owning a vehicle for a person who is employed, 60 years of age and married. (10pts)

c) The answer you got from the previous question is actually greater than 1. Explain why that is. (10pts)

d) Will you be able to test the significance of the coefficients if you were given all the standard errors and/or p-values? Say “yes” or ‘no”, then explain. (10pts)

3. Elaborate, in your own words, the difference between conducting the standard White test and the special case of the White test. (5pts)

Answer 1

Part A:

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

Medica bill for the person who both drinks and smokes:

=1+2(1)+3(1)+4(1)+0

=10

Medica bill for the person who just smokes

=1+2(0)+3(1)+4(0)+0

=4

Difference between the two=10-4=6

Qb). No, because we are not given the alpha or the confidence interval like 95%,90%,99%, etc. Hence, even though we have standard errors given, we cannot test whether the difference is statistically significant or not.

Part B:

Qa). Co-efficient 0.2 is the co-efficient of the probability equation. It shows the relative strength of the variable. So the employment status contributes 0.2 to the overall probability of the person owning a vehicle.

Qb). the probability of owning a vehicle for a person who is employed, 60 years of age, and married is:

=0.3+0.2(1)+.003*(60)+0.4(1)

=1.08.

Qc). It could be because of two reasons:

1. The equation you copied is wrong, or

2. The sample is biased. It could be that the sample consists of people who were employed and with age they saw a rise in income and hence were able to purchase a vehicle. Selecting a broad sample consisting of people of older age group may result in an equation which could give accurate results.

Qd). No, since the alpha or the confidence level is not given, it is not possible.