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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 80

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 auction; a portion of the printout follows:
 PARAMETER  STANDARD  T FOR 0;  VARIABLES  ESTIMATE  ERROR  PARAMETER =0 PROB >TI INTERCEPT 286.429.66X.31.0629.64.0001XX.000067.000075.14.0016\begin{array}{lrrrr}\hline & \text { PARAMETER } & \text { STANDARD } & \text { T FOR 0; } & \\\text { VARIABLES } & \text { ESTIMATE } & \text { ERROR } & \text { PARAMETER }=0 & \text { PROB }>\mid \mathrm{TI} \\\text { INTERCEPT } & 286.42 & 9.66 & & \\\mathrm{X} & .31 & .06 & 29.64 & .0001 \\\mathrm{X} \cdot \mathrm{X} & -.000067 & .00007 & 5.14 & .0016 \\\hline\end{array}

Give the pp -value for testing H0:β2=0H _ { 0 } : \beta _ { 2 } = 0 against Ha:β20H _ { a } : \beta _ { 2 } \neq 0 .


A) .0016.0016
B) .18.18
C) . 36
D) . 05

Correct Answer:

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