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

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; the resulting estimate of $\beta _ { 1 }$ was $- .31$ .
Interpret this estimate of $\beta _ { 1 }$ .

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