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

question 14

True/False

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=β0+β1X+β2X2+ε 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
 Regression Statistics Multiple R 0.994 R Square 0.988 Standard Error 12.42 Observations 12\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}

ANOVAANOVA
dfSS MS F Signifcance  Regression 2115145575733730.0001 Residual 91388154 Total 11116533\begin{array}{lrrrrc}\hline & d f & S S & \text { MS } & F & \text { Signifcance } \\\hline \text { Regression } & 2 & 115145 & 57573 & 373 & 0.0001 \\\text { Residual } & 9 & 1388 & 154 & & \\\text { Total } & 11 & 116533 & & & \\\hline\end{array}


 Coeff  Std Error t Stat  p-value  Intercept 286.429.6629.640.0001 Price 0.310.065.140.0006 Price Sq 0.0000670.000070.950.3647\begin{array}{lrccc}\hline & \text { Coeff } & \text { Std Error } & t \text { Stat } & \text { p-value } \\\hline \text { Intercept } & 286.42 & 9.66 & 29.64 & 0.0001 \\\text { Price } & -0.31 & 0.06 & -5.14 & 0.0006 \\\text { Price Sq } & 0.000067 & 0.00007 & 0.95 & 0.3647\end{array}

-Referring to Table 15-3, a more parsimonious simple linear model is likely to be statistically superior to the fitted curvilinear for predicting sale price (Y).

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A wide range of cognitive biases that influence the responses of participants away from an accurate or truthful response.

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