A Manufacturer of Boiler Drums Wants to Use Regression to Predict

question 70

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: $\quad x _ { 1 } =$ Boiler design pressure (pounds per square inch, i.e., psi)
The simple linear model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$ was fit to the data. A printout for the analysis appears below:

UNWEIGHTED LEAST SQUARES LINEAR REGRESSION OF MANHRS

$\begin{array}{c|c|c|c|c}\text { PREDICTOR } & & & & \\\text { VARIABLES } & \text { COEFFICIENT } & \text { STD ERROR } & \text { STUDENT'S T } & \text { P } \\\hline \text { CONSTANT } & 1.88059 & 0.58380 & 3.22 & 0.0028 \\\text { PRESSURE } & 0.00321 & 0.00163 & 2.17 & 0.0300\end{array}$


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


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

Fill in the blank. At $\alpha = .01$ , there is between man-hours and pressure.

• A) sufficient evidence of a linear relationship
• B) sufficient evidence of a negative linear relationship
• C) sufficient evidence of a positive linear relationship
• D) insufficient evidence of a positive linear relationship

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Definitions:

Mechanism

The detailed step-by-step process or pathway by which a chemical reaction occurs, including the rearrangements of bonds and intermediate stages.

Reaction

A process in which substances interact to form new products, involving the reorganization of atoms or groups of atoms.

Ammonia

A compound of nitrogen and hydrogen with the formula NH3, characterized by its pungent smell and used as a fertilizer and cleaning agent.

2-Phenylethylamine

An organic compound with the formula C8H11N, characterized by a phenyl group attached to an ethylamine.