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 90

Short Answer

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, to obtain a fitted value for the fourth quarter of 2010 using the model, which of the following sets of values should be used in the regression equation? a) $X = 7 , Q _ { 1 } = 0 , Q _ { 2 } = 0 , Q _ { 3 } = 0$
b) $X = 7 , Q _ { 1 } = 1 , Q _ { 2 } = 0 , Q _ { 3 } = 0$
c) $X = 8 , Q _ { 1 } = 0 , Q _ { 2 } = 0 , Q _ { 3 } = 0$
d) $X = 8 , Q _ { 1 } = 1 , Q _ { 2 } = 0 , Q _ { 3 } = 0$

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Definitions:

Crystallized Intelligence

The ability to use learned knowledge and experience, which typically increases with age.

Fluid Intelligence

The potential to employ logical reasoning and find solutions in unique scenarios, not dependent on existing knowledge.

Numeric Ability

The capacity to understand, work with, and reason using numbers, often evaluated in educational and psychological testing.

Procedural Memory

A type of long-term memory that is responsible for knowing how to do things and perform certain tasks.