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, in testing the significance of the coefficient of X in the regression equation (0.012) which has a p-value of 0.0000. Which of the following is the best interpretation of this result?
A) The quarterly growth rate in revenues is significantly different from 0% (α = 0.05).
B) The quarterly growth rate in revenues is not significantly different from 0% (α = 0.05).
C) The quarterly growth rate in revenues is significantly different from 1.2% (α = 0.05).
D) The quarterly growth rate in revenues is not significantly different from 1.2% (α = 0.05).

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, in testing the significance of the coefficient of X in the regression equation (0.012) which has a p-value of 0.0000. Which of the following is the best interpretation of this result?
A) The quarterly growth rate in revenues is significantly different from 0% (α = 0.05). 
B) The quarterly growth rate in revenues is not significantly different from 0% (α = 0.05). 
C) The quarterly growth rate in revenues is significantly different from 1.2% (α = 0.05). 
D) The quarterly growth rate in revenues is not significantly different from 1.2% (α = 0.05).

Quizplus · Accepted Answer

The null hypothesis for testing the significance of the coefficient of X is that there is no relationship between X and the estimated number of contracts in a quarter. The alternative hypothesis is that there is a relationship. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that the quarterly growth rate in revenues is significantly different from 0%.

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