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

question 111

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 atiction; a portion of the printout follows:
$\begin{array}{lrrrrr}\hline \text { SOURCE } & \text { DF } & 55 & \text { MS } & \text { FVALUE } & \text { PROB }>\text { F } \\\text { MODEL } & 2 & 4277160 & 2138579 & 120 & .0005 \\\text { ERROR } & 29 & 514034 & 17725 & & \\\text { TOTAL } & 31 & 4791194 & & &\end{array}$

$\begin{array}{cccc}\text { ROOT MSE } & 133 & \text { R-SQUARE } & 893 \\\text { DEP MEAN } & 1327 & \text { ADJ R-SQ } & .885\end{array}$

$\begin{array}{lrrrr}&\text { PARAMETER }& \text {STANDARD }& \text { T FOR 0: }\\ \text { VARIABLES } & \text { ESTIMATE } & \text { ERROR } & \text { PARAMETER }=0 & \text { PROB }>|T| \\\text { INTERCEPT } & 286.42 & 9.66 & 29.64 & .0001 \\\mathrm{X} & .31 & .06 & 5.14 & .0016 \\\mathrm{X} \cdot \mathrm{X} & -.000067 & .00007 & -0.95 & .3600 \\\hline\end{array}$

An outlier for the model is a clock with a residual that _____ in absolute value. (Fill in the blank.)

• A) exceeds 399
• B) exceeds 133
• C) exceeds .893
• D) is less than 266

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Definitions:

Grade Point Average

A numerical calculation that represents the average value of the accumulated final grades earned in courses over time, typically on a scale from 0 to 4.0.

Semester Grades

The final assessment of a student's performance in their courses over a semester.

Relative Frequency

The ratio of the number of times a particular value or event occurs to the total number of occurrences.

Frequency

The number of times an event or data value occurs.