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 114

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 X (0.012) in the regression equation is:

• A) The annual growth rate in revenues is around 1.2%.
• B) The quarterly growth rate in revenues is around 1.2%.
• C) The quarterly compound growth rate in revenues is around 2.8%.
• D) The annual growth rate in revenues is around 2.8%.

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Definitions:

Cubic Polynomial

A polynomial of degree three, characterized by an equation of the form ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.

Quintic Polynomial

A polynomial of degree five, represented as \(ax^5 + bx^4 + cx^3 + dx^2 + ex + f\) where \(a\), \(b\), \(c\), \(d\), \(e\), and \(f\) are constants and \(a \neq 0\).

Scientific Notation

A way of expressing numbers that are too big or too small to be conveniently written in decimal form, using powers of 10.

Position Function

A mathematical function that describes the position of an object as a function of time, often used in physics to study motion.