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

question 62

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,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 not significantly different than 100% (\(\alpha\) = 0.05).
• B) The quarterly growth rate in the number of contracts is significantly different than 100% (\(\alpha\) = 0.05).
• C) The quarterly growth rate in the number of contracts is significantly different than 0% (\(\alpha\) = 0.05).
• D) The quarterly growth rate in the number of contracts is not significantly different than 0% (\(\alpha\)= 0.05).

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Definitions:

Marginal Cost Pricing

A pricing strategy where the price of a good or service is set equal to the marginal cost of producing one more unit, commonly used in regulated utilities.

Regulatory Agency

A government body responsible for creating and enforcing rules to govern a specific industry or sector.

Social Welfare

Policies and programs designed to improve the well-being of individuals and communities, addressing needs such as health, education, and employment.

Natural Monopoly

A market condition where a single firm can provide a product or service at a lower cost than any potential competitor, often due to high fixed or start-up costs.