Choose the One Alternative That Best Completes the Statement or Answers

question 4

Multiple Choice

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.

Grasp the role of technology and new media in business communication.

Acknowledge the evolution of the workplace environment and the anticipation of cultural diversity and global competition.

Comprehend the significance of business ethics in modern work trends.

Realize the extent of listening involvement in professional settings and its effectiveness.

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Definitions:

Risk-loving

A preference or inclination for taking on risks where the potential for gains outweighs the potential losses, as opposed to risk-aversion.

Risk-averse

describes an individual or entity that prefers to avoid risk and opts for the option with the least uncertainty.

Risk Premium

The additional return expected by an investor for taking on a higher level of risk compared with a risk-free investment.

Utils

A hypothetical unit of measurement used in economics to quantify the amount of utility or satisfaction gained by consuming goods and services.