SCENARIO 16-12
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 74

Multiple Choice

SCENARIO 16-12
A local store developed a multiplicative time-series model to forecast its revenues in future
quarters, using quarterly data on its revenues during the 5-year period from 2009 to 2013. 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 $\hat { Y }$ 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 Scenario 16-12, the best interpretation of the coefficient of Q2 (-0.054) in the regression equation is:

• A) the revenues in the second quarter of a year is approximately 5.4% lower than the average over all 4 quarters.
• B) the revenues in the second quarter of a year is approximately 5.4% lower than it would be during the fourth quarter.
• C) the revenues in the second quarter of a year is approximately 11.69% lower than the average over all 4 quarters.
• D) the revenues in the second quarter of a year is approximately 11.69% lower than it would be during the fourth quarter.

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Definitions:

Identity Relationship

The connection or relation between various aspects of an individual's identity, such as cultural, personal, or social attributes.

Fallacy of Affirming the Consequent

A logical fallacy that occurs when, from an if-then statement, one incorrectly infers the if-part solely from the then-part.

Affirming the Consequent

A logical fallacy in which a conclusion is incorrectly derived from a conditional statement (if A, then B; B, therefore A).

Straw Man Fallacy

A logical fallacy that involves misrepresenting an argument to make it easier to attack.