ABIZ 3080
Fall 2013
Assignment #3
Due Date: 1 Nov. 2013
Answer all of the following questions. If you do not have the text you should borrow one
or use one of the copies on reserve in the Agriculture library. Assignments should be
typewritten or neatly handwritten, and are due at the beginning of class on the due date.
1. This is a continuation of the questions from Assignment #2 that use data on salary and
education from the file salary.dat.
(a) test the null hypothesis that years of education have no effect on starting salary at the
5% level of significance. What alternative hypothesis have you chosen? Why?
2. Again using the data contained in jobs.dat, and the standard errors obtained in the
previous question, construct two 95% interval estimates for 2.
(a) use the first 15 observations for one interval and all 24 observations for the other
interval. What factors contribute to one interval being wider than the other?
3. The Winnipeg Blue Bombers are looking for a budding young econometrician to
forecast beer sales for their home games once they move to the new stadium at U of M,
and have approached you to analyse data for them. They have a fairly simple data set
containing beer sales and outside temperature in degrees Celsius, found in the file
BOMBERS.XLS on the course homepage.
(a) how do beer sales respond to temperature changes?
(b) test the hypothesis that a one degree decrease in temperature will cause beer sales to
decline by 40 dozen.
The football club also wants you to help them set prices for beer. They conducted a
survey of 100 North American stadiums (college and pro) and received 35 responses with
data on price and per- capita beer consumption at games (to remove the effect of stadium
size). The data can be found in the file STADIUM.XLS on the course homepage.
(c) according to the data, what is the price elasticity of demand for beer? Find both an arc
elasticity and a point elasticity.
(d) what proportion of the change in per-capita beer consumption is explained by your
model? How do you think your model could be improved to explain a greater proportion
of the variation in per-capita beer consumption?
4. The file tax.dat on the course homepage contains observations on the gross income and
tax paid for 30 companies in for the 1988 and 1989 tax years.
(a) estimate tax paid as a function of income for the two years. Interpret the slope
parameters you obtain.
(b) construct a 95% confidence interval for the 1989 slope parameter.
(c) calculate the average income for each year and predict the tax paid for those levels of
income. Discuss how the average income and marginal rates compare.
(d) for each year, test the hypothesis that the marginal tax rates is 19%. Do all parts of the
hypothesis tests.
5. Suppose you run the simple linear regression model on 40 observations:
lnYt = β1 + β2lnXt + et
and obtain the following results:
Variable
Intercept
lnXt
Parameter Estimate
(std. error)
6.3738
(1.739)
0.4410
(0.021)
(a) test H0: a 1% increase in the independent variable leads to a 0.40% increase in the
dependent variable. Be sure to carry out all parts of the hypothesis test. Choose a test size
you feel is appropriate.
(b) construct a 90% confidence interval for β2
Please do not hesitate to consult myself or Mr. Choi if you have questions.