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.

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Definitions:

Ethoxide

An alkoxide derived from ethanol, used as a strong base in organic synthesis, with the formula CH3CH2O-.

Sodium Cyanide

A chemical compound with the formula NaCN, highly toxic and used in gold mining and chemical synthesis.

DMSO

Dimethyl sulfoxide, a polar solvent with the formula (CH3)2SO, known for its ability to penetrate biological membranes and used in various chemical and pharmaceutical applications.

Nucleophilic

Describes a chemical species that donates an electron pair to an electrophile to form a chemical bond in a reaction.