Assignment 1: Estimation of Demand
Provide a copy of your written answers by Wednesday, October 21, 2015. You will be
contacted with the details on how, where and when to submit your answers. You can obtain
up to 5 marks counting towards the nal mark for this semester. You should include your
student registration number on each page and the name of your tutor on the
top-right corner of therst page of your work.

Exercise 1 (Simple Linear Regression): In a study of housing demand, the county
assessor is interested in developing a regression model to estimate the market value (i.e.,
selling price) of residential property within his jurisdiction. The assessor feels that the
most important variable a ecting selling price (measured in thousands of dollar) is the
size of the house (measured in hundreds of square feet). He has randomly selected 15
houses and measured both the selling price and size, as shown in the table below.
Size (

100ft2 )

Observation

Selling Price ( 1000)

1

65.2

12.0

2

79.6

20.2

3

111.2

27.0

4

128.0

30.0

5

152.0

30.0

6

81.2

21.4

7

88.4

21.6

8

92.8

25.2

9

156.0

37.2

10

63.2

14.4

11

72.4

15.0

12

91.2

22.4

13

99.6

23.9

14

107.6

26.6

15

120.4

30.7

(a) Plot the data.
(b) Determine the estimated regression line. Give an economic interpretation of the
estimated slope (b) coe cient.
(c) Determine if size is a statistically signi cant variable in estimating selling price.
(d) Calculate the coe cient of determination.
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(e) Perform an F -test of the overall signi cance of the results.
(f) Construct an approximate 95% prediction interval for the selling price of a house
having an area (size) of 15 (hundred) square feet.

Exercise 2 (Multiple Linear Regression): Cascade Pharmaceuticals Company developed the following regression model, using time series data from the past 33 quarters, for
one of its nonprescription cold remedies:
Y =

1:04 + 0:24X1

0:27X2

where Y = quarterly sales (in thousands of cases) of the cold remedy, X1 = Cascade’s
quarterly advertising (in $ 1,000) for the cold remedy, and X2 = competitors’ advertising
for similar products (in $ 1,000).
Additional information concerning the regression model:
sb1 = 0:032 sb2 = 0:070
R2 = 0:64

se = 1:63

F -statistic = 31:402

Durbin-Watson (d) statistic 0:4995
(a) Which of the independent variables (if any) appear to be statistically signi cant (at
the 0.05 level) in explaining sales of the cold remedy?
(b) What proportion of the total variation in sales is explained by the regression equation?
(c) Perform an F -test (at the 0.05 level) of the overall explanatory power of the model.
(d) What conclusions can be drawn from the data about the possible presence of autocorrelation?
(e) How do the results in part (d) a ect your answer to parts (a), (b), and (c)?
(f) What additional statistical information (if any) would you nd useful in the evaluation of this model?

2

Labor Economics , will need an Excel Spreadsheet.

You are in charge of hiring for the sales department of Nature’s Own chemical company. You are choosing between two workers, a “safe” worker who will produce 250 thousand dollars in sales (net of variable costs) in each of the next four years. The “risky” worker produces 500 thousand dollars in annual sales with probability p, and will cost the company 250 thousand dollars in sales with probability (1-p). Both workers will stay with Nature’s Own for one year for sure, and will leave after four years for sure. There is, however, a 50 percent chance that either type of worker will quit between the end of the first and the start of the second period. If they don’t quit at that moment then they will stay for sure till the end of year 4. (Note to the wise: this is a crude way of modeling a declining quit rate over the worker’s career; it is different from the constant quit rate we modeled in class).

If hired, the salary of each type of worker will be $100,000 per year. The discount rate is zero. A risky worker’s “type” (good or bad; i.e. high or low sales) becomes known after the end of his/her first year with Nature’s Own.

a.) Set up a spreadsheet to calculate the firm’s expected present value of hiring each type of worker. Allow for “inputable” values of all the parameters above (the productivities of both worker types in both years, the probability the risky worker is the “good” type, and the probability that workers quit after the first year.

b.) If p = 0.5, which worker should you hire? Is this the worker with the highest expected value of sales in the first year?

c.) Now raise the “riskiness” of the risky worker by raising her sales if she is “good” to 700 thousand, and increasing her net losses if she is “bad” from 250 to 450 thousand dollars. What does this do to her expected value of sales in the first year? Does this change your recommendation on which worker to hire? Why or why not?

d.) Keeping workers’ productivities at the levels in part c above, raise the probability that workers of either type quit after year 1 from .5 to .75. Which worker would you hire now? Why?