1.You decide to estimate the following quarterly sales forecasting model for new boat

sales in your local county:

Qt = a + bt + cD

The equation is estimated using quarterly data on new boat sales in the county from the

3rd quarter of 2001 to the 4th quarter of 2007 (t = 1,…,26). The variable D is a dummy

variable for the second quarter, which is the “season” for selling new boats: D = 1 in the

second quarter, and 0 otherwise. The results of the estimation are:

DEPENDENT VARIALBE:

OBSERVATIONS:

VARIABLE

QT

R-SQUARE F-RATIO

P-VALUE ON F

0.5216

12.54

0.0002

PARAMETER STANDARD

ESTIMATE

ERROR

T-RATIO

P-

INTERCEPT

T

D

241.3

47.52

34.66

26

VALUE

65.36

13.55

10.33

3.69

3.51

3.36

0.0012

0.0019

0.0027

a. Do the statistical estimates indicate a trend in sales? If so, what is the trend in

units per quarter?

b. Do the statistical estimates indicate a seasonal effect on 2nd quarter sales? If

so, what is the seasonal effect in units per quarter?

c. What are the forecasted sales for the 1st quarter of 2008?

d. What are the forecasted sales for the 2nd quarter of 2008?

e. What are the forecasted sales for the 3rd quarter of 2008?

f. What are the forecasted sales for the 4th quarter of 2008?

2. The marketing manager of a large supermarket chain wants to determine how sales

of the soft drinks are affected by shelf space and product placement. The soft drinks

were placed either at the front or back of the aisle. Data collected from a random

sample of 20 equal-sized stores is summarized below.

a. Write out the multiple regression equation.

b. Estimate the regression coefficients using ordinary least squares and interpret them.

c. Predict the weekly sales for a store with 10 feet of shelf space situated at the back of

the aisle.

d. At the 0.05 level of significance, determine whether each independent variable makes

a contribution to the regression model.

Sales

1.6

2.2

Space

5

5

Place

0

1

1.4

1.9

2.4

5

10

10

0

0

0

Place = 1 indicates front of

aisle

Place = 0 indicates back of aisle

2.6

2.3

2.7

2.8

2.6

2.9

3.1

1.9

2.4

2.6

2.3

2.7

1.4

1.9

2.4

10

15

15

15

20

20

20

10

10

10

15

15

5

10

10

1

0

0

1

0

0

1

0

0

1

0

0

0

0

0

Space = feet of shelf space

Sales given in 1000/week