You decide to estimate the following quarterly sales forecasting model for new b
ID: 2496313 • Letter: Y
Question
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 VARIABLE:
QT
R-SQUARE
F-RATIO
P-VALUE ON F
OBSERVATIONS:
26
0.5216
12.54
0.0002
VARIABLE
PARAMETER
STANDARD
ESTIMATE
ERROR
T-RATIO
P-VALUE
INTERCEPT
241.3
65.36
3.69
0.0012
T
47.52
13.55
3.51
0.0019
D
34.66
10.33
3.36
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?
DEPENDENT VARIABLE:
QT
R-SQUARE
F-RATIO
P-VALUE ON F
OBSERVATIONS:
26
0.5216
12.54
0.0002
VARIABLE
PARAMETER
STANDARD
ESTIMATE
ERROR
T-RATIO
P-VALUE
INTERCEPT
241.3
65.36
3.69
0.0012
T
47.52
13.55
3.51
0.0019
D
34.66
10.33
3.36
0.0027
Explanation / Answer
a) Yes, the statistical estimates indicates tht there is a trend in sales as p-value is less than 0.5% which indicates significant relationship between the variables. The trend indicates positive relation as the coefficient ,b ,is positive.
b) yes, it indicates seasonal effect on 2nd quarter sales as p-vale of D is less than 0.5% and the dummy variable that indicates seasonal effect is significant.
c) Qt = 241.3 + 47.52 * 27 = 1524.34
d) Qt = 241.3 + 47.52 * 28 + 34.66 * 1= 1606.52
e) Qt = 241.3 + 47.52 * 29 = 1619.38
f) Qt = 241.3 + 47.52 * 30 = 1666.9
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