1) Health economists have estimated a model of alcohol consumption:
Dˆ i  13.00  11.36 ADVICEi  0.20 EDUCi  2.85DIVSEPi  14.20UNEMPi
(2.12)
t = 5.37
(0.31)
 0.65
(2.55)
1.11
(5.16)
2.75
N= 500, R 2  0.07
Where: Di = number of drinks consumed by the i-th individual in the last two weeks
ADVICEi = a dummy variable equal to 1 if a physician had advised the i-th individual to cut
back on drinking alcohol, 0 otherwise
EDUCi = years of schooling of the i-th individual
DIVSEPi = a dummy variable equal to 1 if the i-th individual was divorced or separated, 0
otherwise
UNEMPi = a dummy variable equal to 1 if the i-th individual was unemployed, 0 otherwise
a) It seems reasonable to expect positive coefficients for DIVSEP and UNEMP. Create and test
appropriate hypotheses for the coefficients of DIVSEP and UNEMP at the 5% level.
b) Create and run a two-sided hypothesis test around zero of the coefficient of EDUC at the 1% level.
Why might a two-sided test be appropriate for this coefficient?
c) Most physicians would expect that if they urged patients to drink less alcohol, that is what the
patients actually do (holding constant the other variables in the equation). Create and test
appropriate hypotheses for the coefficient of ADVICE at the 10% level.
d) Does your answer to part c.) cause you to question whether you should change you hypotheses in
part c.)? Explain.
2) Suppose that you estimate a model of house prices to determine the impact of having a beach front
location on the value of a house. You do some research, and you decide to use the size of the lot instead
of the size of the house for a number of reasons related to theory and data availability. Your results are
(with standard errors in parentheses):
P̂i  40  35.0 LOTi  2.0 AGEi  10.0 BEDi  4.0 FIREi  100 BEACH i
(5.0)
(1.0)
(10.0)
(4.0)
(10.0)
N = 30, R  0.63
2
Where: Pi = the price of the i-th house in thousands of dollars
LOTi = the size of the lot of the i-th house in thousands of square feet
AGEi = the age of the i-th house in years
BEDi = the number of bedrooms in the i-th house
FIREi = a dummy variable for a fireplace (1 = yes for the i-th house)
BEACHi = a dummy for having beach frontage (1 = yes for the i-th house)
a) You expect the variables LOT, BED, and BEACH to have positive coefficients. Create and test the
appropriate hypotheses to evaluate these expectations at the 5% level.
b) You expect AGE to have a negative coefficient. Create and test the appropriate hypotheses to
evaluate these expectations at the 10% level.
c) At first, you expect FIRE to have a positive coefficient, but one of your friends says that fireplaces
are messy and are a pain to keep clean, so you are not sure. Run a two-sided t-test around zero to
test these expectations at the 5% level.
d) What problems appear to exist in your equation? That is, consider the signs and significance of
your coefficients.
e) Which of the problems you outline in part d.) is the most worrisome to you? Explain.
f) What explanation/solution can you think of for this problem?