TABLE 16-13
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 1998 to 2002. The following is the resulting regression equation:
log 1 0 Y ^ = 6.102 + 0.012 X - 0.129 Q 1 - 0.054 Q 2 + 0.098 Q 3
where
Y ^ is the estimated number of contracts in a quarter
X is the coded quarterly value with X = 0 in the first quarter of 1998.
Q 1 is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise.
Q 2 is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise.
Q 3 is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise.
-Referring to Table 16-13, the best interpretation of the coefficient of X (0.012) in the regression equation is
A) the annual growth rate in revenues is around 2.8%.
B) the annual growth rate in revenues is around 1.2%.
C) the quarterly compound growth rate in revenues is around 2.8%.
D) the quarterly growth rate in revenues is around 1.2%.

Question

TABLE 16-13
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 1998 to 2002. The following is the resulting regression equation:
log 1 0 Y ^  = 6.102 + 0.012 X - 0.129 Q 1   - 0.054 Q 2   + 0.098 Q 3 
where
 Y ^  is the estimated number of contracts in a quarter
X is the coded quarterly value with X = 0 in the first quarter of 1998.
Q 1 is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise. 
Q 2  is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise. 
Q 3  is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise.
-Referring to Table 16-13, the best interpretation of the coefficient of X (0.012) in the regression equation is
A) the annual growth rate in revenues is around 2.8%.
B) the annual growth rate in revenues is around 1.2%.
C) the quarterly compound growth rate in revenues is around 2.8%.
D) the quarterly growth rate in revenues is around 1.2%.

Quizplus · Accepted Answer

The coefficient of X in the regression equation represents the quarterly growth rate in revenues. Since it is positive (0.012), it indicates that revenues are growing over time. To interpret this growth rate as an annual or compound growth rate, we need to convert it accordingly. Quarterly compound growth rate can be calculated as (1 + quarterly growth rate)^4 - 1. Using this formula, we get an estimated annual compound growth rate of around 0.028 or 2.8%. Therefore, choice C is the best interpretation.

TABLE 16-13 A Local Store Developed a Multiplicative Time-Series Model to Forecast