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 178

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,the best interpretation of the coefficient of Q₃ (0.098) in the regression equation is:

• A) The revenues in the third quarter of a year is approximately 25.31% higher than the average over all four quarters.
• B) The revenues in the third quarter of a year is approximately 25.31% higher than it would be during the fourth quarter.
• C) The revenues in the third quarter of a year is approximately 9.8% higher than the average over all 4 quarters.
• D) The revenues in the third quarter of a year is approximately 9.8% higher than it would be during the fourth quarter.

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Definitions:

Earnings Rate

The rate at which a company generates income relative to assets, investments, or equity.

Internal Rate of Return

A metric used in financial analysis to estimate the profitability of potential investments, calculated as the rate of return that makes the net present value of all cash flows from a particular project equal to zero.

Compound Interest

A way of calculating interest whereby the charge is based on the initial principal amount as well as on the interest that has accumulated in prior periods of a loan or deposit.

Cash Inflow

Money received by a business, typically from operational, investing, and financing activities.