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

question 98

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,using the regression equation,which of the following values is the best forecast for the number of contracts in the second quarter of 2012?

• A) 391,742
• B) 1,238,797
• C) 4,355,119
• D) 144,212

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Definitions:

Parameter

A numeric characteristic or measure that defines or summarizes a feature of a population or a model, such as a mean or a variance.

Greek Letters

Symbols from the Greek alphabet used in various fields such as mathematics, science, and engineering to represent variables, constants, and parameters.

Sampling Distribution

A statistical distribution that represents the range and frequency of possible outcomes for a statistic if an experiment were repeated many times under similar conditions.

Normally Distributed

Describes a type of continuous probability distribution for a real-valued random variable where the data forms a bell-shaped curve.