TABLE 16-12
A local store developed a multiplicative time-series model to forecast its revenues in future quarters, using quarterly data on its revenues during the 4-year period from 2005 to 2009. The following is the resulting regression equation:
log₁₀ = 6.102 + 0.012 X - 0.129 Q₁ - 0.054 Q₂ + 0.098 Q₃
where is the estimated number of contracts in a quarter.
X is the coded quarterly value with X = 0 in the first quarter of 2005.
Q₁ is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise.
Q₂ is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise.
Q₃ is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise.
-Referring to Table 16-12, the estimated quarterly compound growth rate in revenues is around
A) 1.2%.
B) 2.8%.
C) 12%.
D) 28%.

Question

TABLE 16-12
A local store developed a multiplicative time-series model to forecast its revenues in future quarters, using quarterly data on its revenues during the 4-year period from 2005 to 2009. The following is the resulting regression equation:
log₁₀  = 6.102 + 0.012 X - 0.129 Q₁ - 0.054 Q₂ + 0.098 Q₃
where  is the estimated number of contracts in a quarter.
X is the coded quarterly value with X = 0 in the first quarter of 2005.
Q₁ is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise.
Q₂ is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise.
Q₃ is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise.
-Referring to Table 16-12, the estimated quarterly compound growth rate in revenues is around
A) 1.2%. 
B) 2.8%. 
C) 12%. 
D) 28%.

Quizplus · Accepted Answer

The estimated quarterly compound growth rate in revenues, denoted by G(t), can be found by taking the exponential of the coefficient of the X variable and subtracting 1:
G(t) = e^(0.012) - 1 ≈ 0.0121
To get the quarterly percentage growth rate, we multiply G(t) by 100:
G(t) × 100 ≈ 1.21%
Therefore, the estimated quarterly compound growth rate in revenues is around 1.2%, which is closest to choice B.

TABLE 16-12 A Local Store Developed a Multiplicative Time-Series Model to Forecast