SCENARIO 17-7
as a Project for His Business Statistics Class $$Y _ { i } = \alpha + \beta _ { 1 } X _ { 1 i } + \beta _ { 2 } X _ { 2 i } + \beta _ { 3 } X _ { 3 i } + \varepsilon$$

question 180

Multiple Choice

SCENARIO 17-7
As a project for his business statistics class, a student examined the factors that determined parking
meter rates throughout the campus area. Data were collected for the price per hour of parking, blocks
to the quadrangle, and one of the three jurisdictions: on campus, in downtown and off campus, or
outside of downtown and off campus. The population regression model hypothesized is $$Y _ { i } = \alpha + \beta _ { 1 } X _ { 1 i } + \beta _ { 2 } X _ { 2 i } + \beta _ { 3 } X _ { 3 i } + \varepsilon$$
where
$Y$ is the meter price
$X _ { l }$ is the number of blocks to the quad
$X _ { 2 }$ is a dummy variable that takes the value 1 if the meter is located in downtown and off campus and the value 0 otherwise
$X _ { 3 }$ is a dummy variable that takes the value 1 if the meter is located outside of downtown and off campus, and the value 0 otherwise

The following Excel results are obtained.

$\begin{array}{lr}\hline {\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.9659 \\\text { R Square } & 0.9331 \\\text { Adjusted R Square } & 0.9294 \\\text { Standard Error } & 0.0327 \\\text { Observations } & 58\end{array}$

$\text { ANOVA }$
$\begin{array}{lrrrrr}\hline & D f & \text { SS } & \text { MS } & F & \text { Significance } F \\\hline \text { Regression } & 3 & 0.8094 & 0.2698 & 251.1995 & 0.0000 \\\text { Residual } & 54 & 0.0580 & 0.0010 & & \\\text { Total } & 57 & 0.8675 & & & \\\hline\end{array}$

$\begin{array}{lrrrr}\hline & \text { Coefficients }& \text {Standard Error } &{t \text { Stat }} & {P \text {-value }} \\\hline \text { Intercept } & 0.5118 & 0.0136 & 37.4675 & 2.4904 \\\mathrm{X}_{1} & -0.0045 & 0.0034 & -1.3276 & 0.1898 \\\mathrm{X}_{2} & -0.2392 & 0.0123 & -19.3942 & 0.0000 \\\mathrm{X}_{3} & -0.0002 & 0.0123 & -0.0214 & 0.9829\end{array}$
-Referring to Scenario 17-7, what is the correct interpretation for the estimated coefficient for $X _ { 2 }$ ?

• A) Holding the effect of the other independent variables constant, the estimated mean difference in costs between parking on campus, and parking outside of downtown and off
• Campus is ?$0.24 per hour.
• B) Holding the effect of the other independent variables constant, the estimated mean difference in costs between parking in downtown and off campus, and parking on campus
• Is ?$0.24 per hour.
• C) Holding the effect of the other independent variables constant, the estimated mean difference in costs between parking in downtown and off campus, and parking outside of
• Downtown and off campus is ?$0.24 per hour.
• D) Holding the effect of the other independent variables constant, the estimated mean difference in costs between parking in downtown and off campus, and parking either
• Outside of downtown and off campus or on campus is ?$0.24 per hour.

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Definitions:

Population Proportions

It denotes the fraction or percentage of a population having a particular property or attribute.

Sample Proportions

Measures that represent the fraction of the sample that exhibits a particular attribute or characteristic.

Population Proportions

Fractions or percentages of a population that fall into various categories, often used in polling and survey results.

Estimator

A statistic used to estimate the value of a population parameter.