Instruction 16-4 A Certain Type of Rare Gem Serves as a Status

question 74

Multiple Choice

Instruction 16-4
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 hypothesise 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:
Y = β₀ + β₁X + β₂X² + ^ε
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:
Note: Std. Error = Standard Error
-Referring to Instruction 16-4,and noting that this model includes both a linear and a quadratic term,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 addition of the square term in price.
• C) 98.8% of the total variation in demand can be explained by just the square term in price.
• D) 98.8% of the total variation in demand can be explained by the quadratic relationship between demand and price.

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Definitions:

Middle Adulthood

The stage of life, generally considered to occur from approximately 45 to 65 years of age, marked by increased self-awareness, stability, and concern for the future.

Sibling Relationships

The dynamics and interactions between brothers and sisters, which can impact individuals' social and emotional development.

Intimate Relationships

Close personal connections between individuals, characterized by emotional attachment, love, trust, and physical closeness.

Cultural Differences

Variations in the way of life, traditions, laws, and norms of different societies, influencing how individuals perceive the world and interact with one another.