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 187

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 the fitted value for the first quarter of 2013 using the model, which of the following sets of values should be used in the regression equation? a) $X = 16 , Q _ { 1 } = 1 , Q _ { 2 } = 0 , Q _ { 3 } = 0$
b) $X = 16 , Q _ { 1 } = 0 , Q _ { 2 } = 1 , Q _ { 3 } = 0$
c) $X = 17 , Q _ { 1 } = 1 , Q _ { 2 } = 0 , Q _ { 3 } = 0$
d) $X = 17 , Q _ { 1 } = 0 , Q _ { 2 } = 1 , Q _ { 3 } = 0$

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Definitions:

Increase

To become or make greater in size, amount, intensity, or degree.

Demand Curve

A diagram illustrating the connection between the price of a commodity and the amount of it consumers want over a set period.

Supply Curve

A graphical representation showing the relationship between the price of a good and the quantity of the good that suppliers are willing to sell at different prices, typically upward sloping.

Income

Money received, especially on a regular basis, for work, through investments, or from any other source, used to acquire goods and services.