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

question 29

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.

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Definitions:

Subdivisions

The act of dividing something into smaller parts or sections.

Home Prices

Refers to the cost at which houses are bought and sold in the real estate market.

Null Hypothesis

A default hypothesis in statistical inference that suggests no statistical significance or effect exists within a set of observations.

Significance Level

A threshold in hypothesis testing that determines the probability of rejecting the null hypothesis when it is actually true, commonly denoted as alpha (α).