A consulting firm estimates the following quarterly sales forecasting model Q t
ID: 2928824 • Letter: A
Question
A consulting firm estimates the following quarterly sales forecasting model
Qt=a+bt+cD
The equation is estimated using quarterly data from 2005I–2015III (t = 1,..., 43). The variable D is a dummy variable for the second quarter where:
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:
43
0.8644
127.5
0.0001
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T-RATIO
P-VALUE
INTERCEPT
22.5
9.32
2.41
0.0201
T
1.86
0.55
3.38
0.0016
D
2.0
0.71
2.82
0.0075
1. Given the above, at the 1 percent level of significance, is there a statistically significant trend in sales?
a. Yes, because 0.0016 < 0.01.
b. No, because 0.0016 > 0.001.
c. Yes, because 0.55 > 0.01.
d. Yes, because 1.86 > 0.01.
e. both c and d
2. Given the above, these estimates indicate that the second quarter change in sales is
a. 22.5 units higher in the second quarter than in the other three quarters.
b. 1.86 units higher in the second quarter than in the other three quarters.
c. 2.00 units higher in the second quarter than in the other three quarters.
d. 24.5 units higher in the second quarter than in the other three quarters.
3. Using the estimated trend line above, what is the predicted level of sales in 2016I ?
a. 110.06
b. 106.20
c. 104.34
d. 102.2
e. none of the above
DEPENDENT VARIABLE:
QT
R-SQUARE
F-RATIO
P-VALUE ON F
OBSERVATIONS:
43
0.8644
127.5
0.0001
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T-RATIO
P-VALUE
INTERCEPT
22.5
9.32
2.41
0.0201
T
1.86
0.55
3.38
0.0016
D
2.0
0.71
2.82
0.0075
Explanation / Answer
1. Given the above, at the 1 percent level of significance, is there a statistically significant trend in sales?
Answer : Yes because 0.0016 < 0.01. Option a is correct.
2. Given the above, these estimates indicate that the second quarter change in sales is
Answer Option c is correct. 2.00 units higher in the second quarter than in the other three quarters.
3. Using the estimated trend line above, what is the predicted level of sales in 2016I ?
Answer : Here t for 2016 I = 45 and D = 0
22.5 + 1.86 t+ 2.0 D = 22.5 + 1.86 * 45 = 106.2
Option B is correct.
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