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

question 45

Short Answer

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; the restilting estimate of $\beta _ { 1 }$ was $- 31$ .
Interpret this estimate of $\beta _ { 1 }$ .
A) $\beta _ { 1 }$ is a shift parameter that has no practical interpretation.
B) We estimate the auction price will decrease $\$ .31$ for each additional bidder at the atiction.
C) We estimate the auction price will increase $\$ .31$ for each additional bidder at the auction.
D) We estimate the auction price will be $- \$ .31$ when there are no bidders at the atuction.

• A) \(\beta _ { 1 }\) is a shift parameter that has no practical interpretation.
• B) We estimate the auction price will decrease \(\$ .31\) for each additional bidder at the atiction.
• C) We estimate the auction price will increase \(\$ .31\) for each additional bidder at the auction.
• D) We estimate the auction price will be \(- \$ .31\) when there are no bidders at the atuction.

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