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A Collector of Grandfather Clocks Believes That the Price Received E(y)=β0+β1x+β2x2E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }

Question 101

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) =β0+β1x+β2x2E ( 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:
 SOURCE  DF 55 MS  FVALUE  PROB > F  MODEL 242771602138579120.0005 ERROR 2951403417725 TOTAL 314791194\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}

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

 PARAMETER STANDARD  T FOR 0:  VARIABLES  ESTIMATE  ERROR  PARAMETER =0 PROB >T INTERCEPT 286.429.6629.64.0001X.31.065.14.0016XX.000067.000070.95.3600\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

Correct Answer:

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