SCENARIO 16-14 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 3-year period from 2011 to 2013.The following is the resulting regression equation: where is the estimated number of contracts in a quarter. X is the coded quarterly value with X = 0 in the first quarter of 2011. is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise. Q is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise. is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise.
-Referring to Scenario 16-14, in testing the coefficient of X in the regression equation (0.117)the results were a t-statistic of 9.08 and an associated p-value of 0.0000.Which of the following is the best interpretation of this result?
A)The quarterly growth rate in the number of contracts is significantly different from 0% ( = 0.05).
B)The quarterly growth rate in the number of contracts is not significantly different from 0% ( = 0.05).
C)The quarterly growth rate in the number of contracts is significantly different from 100% ( = 0.05).
D)The quarterly growth rate in the number of contracts is not significantly different from 100% ( = 0.05).

Question

SCENARIO 16-14 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 3-year period from 2011 to 2013.The following is the resulting regression equation:  where  is the estimated number of contracts in a quarter. X is the coded quarterly value with X = 0 in the first quarter of 2011.  is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise. Q  is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise.  is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise.
-Referring to Scenario 16-14, in testing the coefficient of X in the regression equation (0.117)the results were a t-statistic of 9.08 and an associated p-value of 0.0000.Which of the following is the best interpretation of this result?
A)The quarterly growth rate in the number of contracts is significantly different from 0% ( = 0.05). 
B)The quarterly growth rate in the number of contracts is not significantly different from 0% ( = 0.05). 
C)The quarterly growth rate in the number of contracts is significantly different from 100% ( = 0.05). 
D)The quarterly growth rate in the number of contracts is not significantly different from 100% ( = 0.05).

Quizplus · Accepted Answer

The t-statistic of 9.08 and associated p-value of 0.0000 indicate that the coefficient of X (the coded quarterly value) is significantly different from 0. This means that there is a significant quarterly growth rate in the number of contracts, and the quarterly growth rate is not 0%. Therefore, the best interpretation is choice A: "The quarterly growth rate in the number of contracts is significantly different from 0%." The t-statistic of 9.08 means that the coefficient of X (the quarterly variable) is significantly different from 0 at the 0.05 level of significance. This indicates that the quarterly growth rate in the number of contracts is significantly different from 0%.

SCENARIO 16-14 a Contractor Developed a Multiplicative Time-Series Model to Forecast