Instruction 14-5
a Local Store Developed a Multiplicative Time-Series Model $\hat { Y }$

question 150

Multiple Choice

Instruction 14-5
A local store developed a multiplicative time-series model to forecast its revenues in future quarters,using quarterly data on its revenues during the 4-year period from 2005 to 2009.The following is the resulting regression equation:
log 10 $\hat { Y }$ = 6.102 + 0.012 X - 0.129 Q₁ - 0.054 Q₂ + 0.098 Q₃
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 2005.
Q₁ is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise.
Q₂ is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise.
Q₃ is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise.
-Referring to Instruction 14-5,to obtain a forecast for the fourth quarter of 2006 using the model,which of the following sets of values should be used in the regression equation?

• A)X = 8,Q₁ = 1,Q₂ = 0,Q₃ = 0
• B)X = 8,Q₁ = 0,Q₂ = 0,Q₃ = 0
• C)X = 7,Q₁ = 1,Q₂ = 0,Q₃ = 0
• D)X = 7,Q₁ = 0,Q₂ = 0,Q₃ = 0

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Definitions:

Marginal Revenue

The boost in income derived from the sale of an extra unit of a product or service.

Marginal Cost

The additional cost incurred in the production of one extra unit of a good or service.

Marginal Profit

The additional profit gained from producing or selling one more unit of a good or service.

MR < MC

A condition where marginal revenue is less than marginal cost, suggesting that a firm should reduce its output to maximize profit.