A certain type of rare gem serves as a status symbol for many of its owners. In

Question

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 owners believe they will gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = ß0 + ß1X + ß2X2 + e
where Y = demand (in thousands) and X = retail price per carat.

This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.994
R square 0.988
Standard error 12.42
Observations 12

ANOVA
df SS MS F Significance F
Regression 2 115145 57573 373 0.0001
Residual 9 1388 154
Total 11 116533

Coeff Std Error t Stat p-value
Intercept 286.42 9.66 29.64 0.0001
Price -0.31 0.06 -5.14 0.0006
Price Sq 0.000067 0.00007 0.95 0.3647

Referring to Table 15-2, what is the correct interpretation of the coefficient of multiple determination?
A) 98.8% of the total variation in demand can be explained by just the square term in price.
B) 98.8% of the total variation in demand can be explained by the quadratic relationship between demand and price.
C) 98.8% of the total variation in demand can be explained by the addition of the square term in price.
D) 98.8% of the total variation in demand can be explained by the linear relationship between demand and price.

Explanation / Answer

Correct option: D) 98.8% of the total variation in demand can be explained by the linear relationship between demand and price.

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