Assignment 1: Estimation of Demand Provide a copy of your written answers by Wednesday, October 21, 2015.

| November 24, 2016

Question
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 the

rst 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?

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