Instruction 16-2
a Certain Type of Rare Gem Serves as a Status

question 10

Multiple Choice

Instruction 16-2
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:
$\begin{array}{l|l|l|l|l|l|}\hline \text { SUMMARY } & & \\\hline \text { Regression } & \text { Statistics } & \\\hline \text { Multiple R } & & 0.994 \\\hline \text { R Square } & & 0.988 \\\hline \text { Std. Error } & & 12.42 \\\hline \text { Observations } & & 12 \\\hline\\\hline\text { ANOVA }\\\hline& \text { If } & \text { SS } & \text { MS } & F & \text { Sigưf F } \\\hline \text { Regression } & 2 & 115145 & 57573 & 373 & 0.0001 \\\hline \text { Residual } & 9 & 1388 & 154 & & \\\hline \text { Total } & 11 & 116533 & & & \\\hline\\\hline& \text { Coeff } & \text { StdError } & \text { Stat } & P \text {-Value } \\\hline \text { Intercept } & 286.42 & 9.66 & 29.64 & 0.0001 \\\hline \text { Price } & 0.31 & 0.06 & -5.14 & 0.0006 \\\hline \text { Price Sq } & 0.000067 & 0.00007 & 0.95 & 0.3647\\\hline\end{array}$ Note: Std.Error = Standard Error
-Referring to Instruction 16-2,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:

Sales Collection

The process of retrieving payment for goods or services provided, typically managed through invoicing and accounts receivable procedures.

Operating Cycle

The period between the acquisition of inventory and the collection of cash from receivables, indicating the efficiency of a company's operations.

Inventory Period

The duration of time goods remain in inventory before being sold.

Accounts Receivable Period

The accounts receivable period is the average time it takes for a business to receive payments owed by its customers for goods or services sold on credit.