TABLE 15-3
a Certain Type of Rare Gem Serves as a Status

question 4

Multiple Choice

TABLE 15-3
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:

$Y=\beta_{0}+\beta_{1} X+\beta_{2} X^{2}+\varepsilon$

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
$\begin{array}{lc}\text {Regression Statistics}\\\hline \text { Multiple R } & 0.994 \\\text { R Square } & 0.988 \\\text { Standard Error } & 12.42 \\\text { Observations } & 12 \\\hline\end{array}$

$\text {ANOVA}$
$\begin{array}{lrrrrc} \hline& d f & S S & \text { MS } & F & \text { Significance } \\\hline \text { Regression } & 2 & 115145 & 57573 & 373 & 0.0001 \\\text { Residual } & 9 & 1388 & 154 & & \\\text { Total } & 11 & 116533 & & & \\\hline\end{array}$


$\begin{array}{lrccc} & \text { Coeff } & \text { Std Error } & t \text { Stat } & p \text {-value } \\\hline \text { Intercept } & 286.42 & 9.66 & 29.64 & 0.0001 \\\text { Price } & -0.31 & 0.06 & -5.14 & 0.0006 \\\text { Price } S q & 0.000067 & 0.00007 & 0.95 & 0.3647 \\\hline\end{array}$


-Referring to Table 15-3, does there appear to be significant upward curvature in the response curve relating the demand (Y) and the price (X) at 10% level of significance?

• A) No, since the p-value for the test is greater than 0.10.
• B) Yes, since the value of þ2 is positive.
• C) Yes, since the p-value for the test is less than 0.10.
• D) No, since the value of þ2 is near 0.

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