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

question 15

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:
$\begin{array}{|l|l|l|l|l|l|}\text { SUMMARY } &output & \\\hline \text { Regression } & \text { Statistics } & \\\hline \text { Multiple R } & & 0.994 \\\hline \text { R Square } & & 0.988 \\\hline \text { Std. Error } & & 12.42 \\\hline \text { Observations } & & 12\\\hline\\\hline\text { ANOVA }\\\hline & \text { dff } & \text { SS } & \text { MS } & F & \text { Siguif } F \\\hline \text { Regression } & 2 & 115145 & 57573 & 373 & 0.0001 \\\hline \text { Residual } & 9 & 1388 & 154 & & \\\hline \text { Total } & 11 & 116533 & & &\\\hline\\\hline & \text { Coeff } & \text { StdError } & \text { t Stat } & \text { P-Value } \\\hline \text { Intercept } & 286.42 & 9.66 & 29.64 & 0.0001 \\\hline \text { Price } & -0.31 & 0.06 & -5.14 & 0.0006 \\\hline\text { Price Sq } & p .000067 & p .00007 & p .95 & p .3647\\\hline\end{array}$ Note: Std.Error = Standard Error
-Referring to Instruction 16-2,what is the value of the test statistic for testing whether the quadratic term is necessary in fitting in the response curve relating the demand (Y) and the price (X) ?

• A)-5.14
• B)0.95
• C)373
• D)None of the above.

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Definitions:

Accrued Interest

Interest that has been incurred but not yet paid over a specified period, typically relating to bonds or loans.

Bond Interest Rate

The percentage of interest that bond issuers must pay to bondholders, typically expressed as an annual rate.

Semiannually

Occurring twice a year; used to describe the frequency with which certain financial or operational events take place, such as interest payments on bonds.

Equity Method

An accounting technique used to record an investor's proportional share of the net income and losses of an investee company in which the investor has significant influence but not full control.