Create a Confidence Interval for the Slope of a Regression $= 7.67 - 3.30$

question 15

Multiple Choice

Create a confidence interval for the slope of a regression equation.
-As the carbon content in steel increases, its ductility tends to decrease. A researcher at
A steel company measures carbon content and ductility for a sample of 15 types of steel.
Based on these data he obtained the following regression results. The regression equation is
Ductility $= 7.67 - 3.30$ Carbon Content

$\begin{array} { l r r r r } \text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \\ \text { Constant } & 7.671 & 1.507 & 5.09 & 0.000 \\ \text { Carbon Content } & - 3.296 & 1.097 & - 3.01 & 0.010 \end{array}$
$$S = 2.36317 \quad \mathrm { R } - \mathrm { Sq } = 41.0 \% \quad \mathrm { R } - \mathrm { Sq } ( \mathrm { adj } ) = 36.5 \%$$
The 95% confidence interval for the slope of the regression equation is

• A) -5.456 to -1.136
• B) -4.393 to -2.199
• C) 6.164 to 9.178
• D) -5.666 to -0.926
• E) 2.581 to 12.761

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Definitions:

Collusive Agreements

Secret or illegal cooperation or conspiracy, especially between competing entities, to cheat or deceive others.

Monopolist

A market participant, individual, or company that holds exclusive control over the supply of a particular good or service, potentially manipulating prices.

Competitive Price-Searcher

A market structure where firms have some control over the price because their products are differentiated, and consumers search for the best prices among competitors.

Long-Run Economic Profit

The excess revenue over costs, including opportunity costs and explicit costs, that a firm realizes when all inputs are considered variable, typically assumed in a period where firms can enter or exit the industry.