SCENARIO 15-1 A certain type of rare gem serves as a status symbol for many of its owners.In theory, for low prices, the demand increases, and it 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 gain in obtaining the gem.Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model: 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
-Referring to Scenario 15-1, what is the correct interpretation of the coefficient of multiple determination?
A)98.8% of the total variation in demand can be explained by the linear relationship between demand and 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 just the square term in price.

Question

SCENARIO 15-1 A certain type of rare gem serves as a status symbol for many of its owners.In theory, for low prices, the demand increases, and it 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 gain in obtaining the gem.Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:  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   
-Referring to Scenario 15-1, what is the correct interpretation of the coefficient of multiple determination?
A)98.8% of the total variation in demand can be explained by the linear relationship between demand and 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 just the square term in price.

Quizplus · Accepted Answer

The coefficient of multiple determination, R-squared, measures the proportion of variation in the response variable (demand in this case) that can be explained by the independent variables (price and price squared). A value of 0.988 indicates that 98.8% of the total variation in demand can be explained by the quadratic relationship between demand and price. The coefficient of multiple determination (R-squared) indicates the proportion of variation in the dependent variable (demand) that can be explained by the independent variable (price) in the model. In this case, the R-squared value of 0.988 indicates that 98.8% of the total variation in demand can be explained by the quadratic relationship between demand and price.

SCENARIO 15-1 a Certain Type of Rare Gem Serves as a Status