A Manufacturer of Boiler Drums Wants to Use Regression to Predict

question 52

Multiple Choice

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: $\quad y =$ Number of man-hours required to erect the drum
PRESSURE: $\quad x =$ Boiler design pressure (pounds per square inch, i.e., psi)
The simple linear model $E ( y ) = \beta 1 + \beta 1 x$ was fit to the data. A printout for the analysis appears below:
UNWEIGHTED LEAST SQUARES LINEAR REGRESSION OF MANHRS
$\begin{array}{c|c|c|c|c}\text { PREDICTOR } & & & & \\\text { VARIABLES } & \text { COEFFICIENT } & \text { STD ERROR } & \text { STUDENTST } & \text { P } \\\hline \text { CONSTANT } & 1.88059 & 0.58380 & 3.22 & 0.0028 \\\text { PRESSURE } & 0.00321 & 0.00163 & 2.17 & 0.0300\end{array}$


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


Give a practical interpretation of the coefficient of determination, $r ^ { 2 }$ .

• A) Approximately \(95 \%\) of the actual man-hours required to build a drum will fall within 43 hours of their predicted values.
• B) We are \(43 \%\) confident that the design pressure will be a useful predictor of number of man-hours required to build a steam drum.
• C) About \(43 \%\) of the sample variation in number of man-hours can be explained by the simple linear model.
• D) About \(2.06 \%\) of the sample variation in number of man-hours can be explained by the simple linear model.

---

Definitions:

Financial Leverage

Employing the use of debt to boost the prospective profits of an investment, which in turn escalates the risk of experiencing a loss.

Debt-To-Equity Ratio

The ratio portraying the financial interplay between shareholder equity and debt in the capital structure for assets.

Net New Bonds

The total value of newly issued bonds minus the bonds that have matured or been bought back by the issuer within a specific period.

Operating Cash Flow

Represents the amount of cash generated by a company's regular business operations.