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

question 27

True/False

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,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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Definitions:

Superiority Complex

A psychological defense mechanism in which an individual exaggerates their own abilities and worth in order to overcome feelings of inferiority.

Idealized Self

A version of oneself that represents the standards of perfection, success, and attractiveness set by oneself or by societal expectations, often unattainable and leading to dissatisfaction.

Bowlby and Ainsworth

Refers to John Bowlby and Mary Ainsworth, psychologists known for their work in developing attachment theory.

Birth Order

The theory that the order in which a child is born into a family can influence their personality and psychological development.