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

question 61

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

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Definitions:

Crown

A term used in legal contexts to denote authority and power of the state, or the monarch in countries with a monarchy.

Mineral Rights

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A thing attached to land or to a building or to another fixture attached to the land.