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

question 177

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 constant 3.37 in the regression equation is:

• A) The fitted value for the first quarter of 2008, prior to seasonal adjustment, is log₁₀ 3.37.
• B) The fitted value for the first quarter of 2008, after seasonal adjustment, is 10^3.37.
• C) The fitted value for the first quarter of 2008, after seasonal adjustment, is log₁₀ 3.37.
• D) The fitted value for the first quarter of 2008, prior to seasonal adjustment, is 10^3.37.

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Definitions:

Sign Test Applications

The uses of a nonparametric test that is used to evaluate the difference between the medians of two paired samples.

Normal Approximation

A method used to approximate the distribution of various sample statistics to the normal distribution under certain conditions.

Nonzero Differences

Refers to the outcomes in statistical analyses where the differences between compared measures or values are not equal to zero, indicating variability or effect.

Binomial Distribution

The binomial distribution is a probability distribution that summarizes the likelihood of obtaining a fixed number of successes in a fixed number of trials in a binary context, where there are only two possible outcomes.