A Collector of Grandfather Clocks Believes That the Price Received $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }$$

question 29

Multiple Choice

A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant) rate. Thus, the model proposed to best explain auction price (y, in dollars) by number of bidders (x) is the quadratic model $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }$$
This model was fit to data collected for a sample of 32 clocks sold at auction; a portion of the printout follows:
$\begin{array}{lrrrr}\hline &\text { PARAMETER }& \text {STANDARD }& \text { T FOR 0: }\\\text { VARIABLES } & \text { ESTIMATE } & \text { ERROR } & \text { PARAMETER }=0 & \text { PROB }>|T|\\\text { INTERCEPT } & 286.42 & 9.66 & 29.64 & .0001 \\\mathrm{X} & -.31 & .06 & -5.14 & .0016 \\\mathrm{X} \cdot \mathrm{X} & .000067 & .00007 & .95 & .3600 \\\hline\end{array}$

Find the $p$ -value for testing $H _ { 0 } : \beta _ { 2 } = 0$ against $H _ { \mathbf { a } } : \beta _ { 2 } > 0$ .

• A) .18
• B) .36
• C) .0016
• D) .05

Conduct and interpret hypothesis tests for population slope and correlation coefficient in linear regression.

Calculate and interpret the Pearson correlation coefficient in the context of linear relationships.

Understand the impact of sample size, standard error, and x value on the width of confidence intervals.

Predict values using regression analysis and estimate intervals with a given confidence level.

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Definitions:

Joint Venture

A venture that operates in a foreign country through co-ownership by foreign and local partners.

Organic Forms

Organizational structures that are flexible, decentralized, and characterized by less formal rules and procedures, often adapting quickly to changes.

Bureaucratic Structures

Organizational forms that are characterized by a hierarchical arrangement of jobs, reliance on formal rules and regulations, and a clear distinction of labor.

Environmental Uncertainty

A lack of information regarding what exists in the environment and what developments may occur.