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 109

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,to obtain a forecast for the first quarter of 2009 using the model,which of the following sets of values should be used in the regression equation?

• A) X = 16, Q₁ = 1, Q₂ = 0, Q₃ = 0
• B) X = 17, Q₁ = 1, Q₂ = 0, Q₃ = 0
• C) X = 17, Q₁ = 0, Q₂ = 1, Q₃ = 0
• D) X = 16, Q₁ = 0, Q₂ = 1, Q₃ = 0

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Definitions:

Price Elasticity

A measure of how much the quantity demanded of a good responds to a change in the price of that good, indicating the sensitivity of consumers to price changes.

Demand Curve

A graph showing the relationship between the price of a good or service and the quantity demanded for it at those prices, typically downward sloping.

Law of Diminishing

A principle that states the incremental utility or benefit gained from consuming additional units of a good or service tends to decrease with each additional unit consumed.

Marginal Utility

The additional utility, or satisfaction, derived from consuming an additional unit of a good.