Choose the one alternative that best completes the statement or answers the question.
-A manufacturer of boiler drums wants to use regression to predict the number of man-hours needed to erect drums in the future. The manufacturer collected a random sample of 35 boilers and measured the following two variables:
MANHRS: $y$ = Number of man-hours required to erect the drum
PRESSURE: $\mathrm { x } _ { 1 } =$ Boiler design pressure (pounds per square inch, i.e., psi)
Initially, the simple linear model $\mathrm { E } ( \mathrm { y } ) = \beta _ { 1 } + \beta _ { 1 \mathrm { x } 1 }$ was fit to the data. A printout for the analysis appears below:
UNWEIGHTED LEAST SQUARES LINEAR REGRESSION OF MANHRS
$\begin{array}{c|c|c|c|c}
\text { PREDICTOR } & & & & \
\text { VARIABLES } & \text { COEFFICIENT } & \text { STD ERROR } & \text { STUDENT'ST } & \mathrm{P} \
\hline \text { CONSTANT } & 1.88059 & 0.58380 & 3.22 & 0.0028 \
\text { PRESSURE } & 0.00321 & 0.00163 & 2.17 & 0.0300
\end{array}$

$\begin{array} { l l l l } \text { R-SQUARED } & 0.4342 & \text { RESID. MEAN SQUARE (MSE) } & 4.25460 \ \text { ADJUSTED R-SQUARED } & 0.4176 & \text { STANDARD DEVIATION } & 2.06267 \end{array}$

$\begin{array}{l|r|c|c|c|c}
\text { SOURCE } & \text { DF } & \text { SS } & \text { MS } & \mathrm{F} & \mathrm{P} \
\hline \text { REGRESSION } & 1 & 111.008 & 111.008 & 5.19 & 0.0300 \
\text { RESIDUAL } & 34 & 144.656 & 4.25160 & & \
\text { TOTAL } & 35 & 255.665 & & &
\end{array}$

Give a practical interpretation of the coefficient of determination, $\mathrm { R } ^ { 2 }$.
A) About $43 \%$ of the sample variation in number of man-hours can be explained by the simple linear model.
B) $\mathrm { y } = 1.88 + 0.00321 \mathrm { x }$ will be correct $43 \%$ of the time.
C) Man hours needed to erect drums will be associated with boiler design pressure $43 \%$ of the time.
D) About $2.06 \%$ of the sample variation in number of man-hours can be explained by the simple linear model.

Question

Choose the one alternative that best completes the statement or answers the question.
-A manufacturer of boiler drums wants to use regression to predict the number of man-hours needed to erect drums in the future. The manufacturer collected a random sample of 35 boilers and measured the following two variables:
MANHRS: $y$ = Number of man-hours required to erect the drum
PRESSURE: $\mathrm { x } _ { 1 } =$ Boiler design pressure (pounds per square inch, i.e., psi)
Initially, the simple linear model $\mathrm { E } ( \mathrm { y } ) = \beta _ { 1 } + \beta _ { 1 \mathrm { x } 1 }$ was fit to the data. A printout for the analysis appears below:
UNWEIGHTED LEAST SQUARES LINEAR REGRESSION OF MANHRS
$\begin{array}{c|c|c|c|c}
\text { PREDICTOR } & & & & \
\text { VARIABLES } & \text { COEFFICIENT } & \text { STD ERROR } & \text { STUDENT'ST } & \mathrm{P} \
\hline \text { CONSTANT } & 1.88059 & 0.58380 & 3.22 & 0.0028 \
\text { PRESSURE } & 0.00321 & 0.00163 & 2.17 & 0.0300
\end{array}$

$\begin{array} { l l l l } \text { R-SQUARED } & 0.4342 & \text { RESID. MEAN SQUARE (MSE) } & 4.25460 \ \text { ADJUSTED R-SQUARED } & 0.4176 & \text { STANDARD DEVIATION } & 2.06267 \end{array}$

$\begin{array}{l|r|c|c|c|c}
\text { SOURCE } & \text { DF } & \text { SS } & \text { MS } & \mathrm{F} & \mathrm{P} \
\hline \text { REGRESSION } & 1 & 111.008 & 111.008 & 5.19 & 0.0300 \
\text { RESIDUAL } & 34 & 144.656 & 4.25160 & & \
\text { TOTAL } & 35 & 255.665 & & &
\end{array}$

Give a practical interpretation of the coefficient of determination, $\mathrm { R } ^ { 2 }$.
A) About $43 \%$ of the sample variation in number of man-hours can be explained by the simple linear model.
B) $\mathrm { y } = 1.88 + 0.00321 \mathrm { x }$ will be correct $43 \%$ of the time.
C) Man hours needed to erect drums will be associated with boiler design pressure $43 \%$ of the time.
D) About $2.06 \%$ of the sample variation in number of man-hours can be explained by the simple linear model.

Quizplus · Accepted Answer

The coefficient of determination, $R^2$, indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. In this case, $43\%$ of the variance in man-hours is explained by the model that includes boiler design pressure.

Choose the One Alternative That Best Completes the Statement or Answers