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 234

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, the best interpretation of the constant 6.102 in the regression equation is: a) the fitted value for the first quarter of 2009 , prior to seasonal adjustment, is $\log _ { 10 } ( 6.102 )$ .
b) the fitted value for the first quarter of 2009 , after to seasonal adjustment, is $\log _ { 10 } ( 6.102 )$ .
c) the fitted value for the first quarter of 2009 , prior to seasonal adjustment, is $10 ^ { 6.102 }$ .
d) the fitted value for the first quarter of 2009 , after to seasonal adjustment, is $10 ^ { 6.102 }$ .

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Definitions:

Economic Payoff

The financial return or reward received from an investment or decision, measured in terms of profit or loss.

Equity

Fairness; everyone gets his or her fair share. Since people can disagree about what is “fair,” equity is not as well defined a concept as efficiency.

Rational Decision

The choice made by logically considering all available information, potential costs, and benefits to achieve the optimal outcome.

Bounded Rationality

A concept suggesting that decision-making is limited by the information available, cognitive limitations of the mind, and the finite amount of time available to make a decision.