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:

Property Tax Rates

The percentage of a property's assessed value that is charged as tax by local governments to fund public expenses.

Break-even Point

The sales level at which total revenues equate to total costs, resulting in no profit or loss, indicating the minimum sales necessary to cover all expenses.

Fixed Costs

Expenses that do not change with the level of production or sales activity, such as rent, salaries, and insurance premiums.

Unit Contribution Margin

The difference between the selling price per unit and the variable cost per unit, indicating how much each unit sold contributes to fixed costs and profits.