Instruction 14-6
a Local Store Developed a Multiplicative Time-Series Model $$\log _ { 10 } \hat { Y } = 6.102 + 0.012 X - 0.129 Q _ { 1 } - 0.054 Q _ { 2 } + 0.098 Q _ { 3 }$$

question 7

Multiple Choice

Instruction 14-6
A local store developed a multiplicative time-series model to forecast its revenues in future quarters, using quarterly data on its revenues during the four-year period from 2005 to 2009. The following is the resulting regression equation:
$$\log _ { 10 } \hat { Y } = 6.102 + 0.012 X - 0.129 Q _ { 1 } - 0.054 Q _ { 2 } + 0.098 Q _ { 3 }$$
Where
$X$ is the coded quarterly value with $X = 0$ in the first quarter of 2005 .
$Q _ { 1 }$ 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 14-6,in testing the significance of the coefficient of X in the regression equation (0.012) which has a p-value of 0.0000,which of the following is the best interpretation of this result?

• A) The quarterly growth rate in revenues is significantly different than 0% (\(\alpha\) = 0.05).
• B) The quarterly growth rate in revenues is not significantly different than 1.2% (\(\alpha\) = 0.05).
• C) The quarterly growth rate in revenues is not significantly different than 0% (\(\alpha\)= 0.05).
• D) The quarterly growth rate in revenues is significantly different than 1.2% (\(\alpha\) = 0.05).

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Definitions:

Confidence Interval

A range of values derived from sample data that is likely to cover the true value of an unknown population parameter, expressed at a given confidence level (e.g., 95%).

High Blood Pressure

A medical condition where the blood pressure in the arteries is persistently elevated, which can lead to serious health issues if not managed properly.

Margin of Error

An expression of the amount of random sampling error in a survey's results, which describes how closely the sample estimate matches the true value in the whole population.

Liberal Party

A political party that generally advocates for policies promoting social welfare, individual rights, and government intervention in the economy to promote social justice.