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 constant 6.102 in the regression equation is A) the fitted value for the first quarter of 1998, after to seasonal adjustment, is 10^6.102. B) the fitted value for the first quarter of 1998, prior to seasonal adjustment, is log₁₀(6.102). C) the fitted value for the first quarter of 1998, prior to seasonal adjustment, is 10^6.102. D) the fitted value for the first quarter of 1998, after to seasonal adjustment, is log₁₀(6.102).

Question

Quizplus · Accepted Answer

The constant in a regression equation represents the fitted value when all the independent variables are equal to zero. In this case, all the independent variables are dummy variables that represent the quarters of the year. When all the dummy variables are equal to zero, it means that we are in the first quarter of 1998. Therefore, the constant 6.102 represents the fitted value for the first quarter of 1998, prior to seasonal adjustment.

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