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Mathematics Clinic => Statistics => Topic started by: frankwu on Feb 14, 2020

Title: A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low ...
Post by: frankwu on Feb 14, 2020

A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model

E(y) = β₀ + β₁x + β₂x²

where y = Demand (in thousands) and x = Retail price per carat (dollars).

This model was fit to data collected for a sample of 12 rare gems.



Does there appear to be upward curvature in the response curve relating y (demand) to x (retail price)?
◦ No, since the value of β₂ is near 0.
◦ Yes, since the p-value for the test is less than .01.
◦ Yes, since the value of β₂ is positive.
◦ No, since the p-value for the test is greater than .10.

Title: A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low ...
Post by: Melissahxx on Feb 14, 2020

No, since the p-value for the test is greater than .10.

Title: Re: A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low
Post by: EJ Yang on Oct 21, 2020

thank you