Question

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 2010 to 2012. The following is the resulting regression equation: ln = 3.37 + 0.117 X - 0.083 Q1 + 1.28 Q2 + 0.617 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 2010 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 Using the regression equation, which of the following values is the best forecast for the number of contracts in the third quarter of 2013?A. The quarterly growth rate in the number of contracts is significantly different from 100% (? = 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 0% (? = 0.05).
D. The quarterly growth rate in the number of contracts is not significantly different from 100% (? = 0.05).

Answer 1

There is a missing content in the question.

After the statements and before the the options given; there is an omitted content which says:

Referring to Table 16-5, 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?

Answer:

C. The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05).

Step-by-step explanation:

From the given question:

The resulting regression equation can be represented as:

$\hat Y = 3.37 + 0.117 X - 0.083 Q_1 + 1.28 Q_2 + 0.617Q_3$

where;

the estimated number of contracts in a quarter X is the coded quarterly value with X = 0

the first quarter of 2010 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

Our null and alternative hypothesis can be stated as;

Null hypothesis :

$H_0 :$  The quarterly growth rate in the number of contracts is not  significantly different from 0% (? = 0.05)

$H_a:$  The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05)

The decision rule is to reject the null hypothesis if the p-value is less than 0.05.

From the missing omitted part we added above; we can see that the   t-statistics value = 9.08 and the p-value = 0.000 .

Conclusion:

Thus; we reject the null hypothesis and accept the alternative hypothesis. i.e

The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05)