Instruction 14-5
a Contractor Developed a Multiplicative Time-Series Model to Forecast

question 1

Multiple Choice

Instruction 14-5
A contractor developed a multiplicative time-series model to forecast the number of contracts in future quarters, using quarterly data on number of contracts during the three-year period from 2008 to 2010. The following is the resulting regression equation:
$$\log _ { 10 } \hat { Y } = 3.37 + 0.117 X - 0.083 Q _ { 1 } + 1.28 Q _ { 2 } + 0.617 Q _ { 3 }$$
Where
$\hat { Y }$ is the estimated number of contracts in a quarter.
$X$ is the coded quarterly value with $X = 0$ in the first quarter of 2008 .
$Q _ { 1 }$ 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 Instruction 14-5,the best interpretation of the coefficient of Q₃ (0.617) in the regression equation is:

• A) The number of contracts in the third quarter of a year is approximately 314% higher than the average over all four quarters.
• B) The number of contracts in the third quarter of a year is approximately 62% higher than it would be during the fourth quarter.
• C) The number of contracts in the third quarter of a year is approximately 62% higher than the average over all four quarters.
• D) The number of contracts in the third quarter of a year is approximately 314% higher than it would be during the fourth quarter.

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