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:
$$Y = B _ { 0 } + B _ { 1 } X + B_ { 2 } X ^ { 2 } + \varepsilon$$
where Y = demand (in thousands) and X = retail price per carat.
$$\begin{array} { | l | l | l | l | l | l | }
\hline \text { SUMMARY } & \text { OUTPUT } & & & & \
\hline \text { Regression } & \text { Statistics } & & & & \
\hline \text { Multiple R } & & 0.994 & & & \
\hline \text { R Square } & & 0.988 & & & \
\hline \text { Std. Error } & & 12.42 & & & \
\hline \text { Observations } & & 12 & & & \
\hline & & & & & \
\hline \text { ANOVA } & & & & & \
\hline & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { Signif F } \
\hline \text { Regression } & 2 & 115,145 & 57,573 & 373 & 0.0001 \
\hline \text { Residual } & 9 & 1,388 & 154 & & \
\hline \text { Total } & 11 & 116,533 & & & \
\hline & & & & & \
\hline & \text { Coeff } & \text { Std. Error } & \text { t Stat } & P \text {-Value } & \
\hline \text { Intercept } & 286.42 & 9.66 & 29.64 & 0.0001 & \
\hline \text { Price } & - 0.31 & 0.06 & - 5.14 & 0.0006 & \
\hline \text { Price Sq } & 0.000067 & 0.00007 & 0.95 & 0.3647 & \
\hline
\end{array}$$ 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:
-Referring to Instruction 16-1,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

Question

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:
 $$Y = B _ { 0 } + B _ { 1 } X + B_ { 2 } X ^ { 2 } + \varepsilon$$ 
where Y = demand (in thousands) and X = retail price per carat.
 $$\begin{array} { | l | l | l | l | l | l | } 
\hline \text { SUMMARY } & \text { OUTPUT } & & & & \
\hline \text { Regression } & \text { Statistics } & & & & \
\hline \text { Multiple R } & & 0.994 & & & \
\hline \text { R Square } & & 0.988 & & & \
\hline \text { Std. Error } & & 12.42 & & & \
\hline \text { Observations } & & 12 & & & \
\hline & & & & & \
\hline \text { ANOVA } & & & & & \
\hline & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { Signif F } \
\hline \text { Regression } & 2 & 115,145 & 57,573 & 373 & 0.0001 \
\hline \text { Residual } & 9 & 1,388 & 154 & & \
\hline \text { Total } & 11 & 116,533 & & & \
\hline & & & & & \
\hline & \text { Coeff } & \text { Std. Error } & \text { t Stat } & P \text {-Value } & \
\hline \text { Intercept } & 286.42 & 9.66 & 29.64 & 0.0001 & \
\hline \text { Price } & - 0.31 & 0.06 & - 5.14 & 0.0006 & \
\hline \text { Price Sq } & 0.000067 & 0.00007 & 0.95 & 0.3647 & \
\hline
\end{array}$$ 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:
-Referring to Instruction 16-1,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

Quizplus · Accepted Answer

The test statistic for testing whether the quadratic term is necessary is given by the t Stat for the "Price Sq" row, which is 0.95.

A Certain Type of Rare Gem Serves as a Status Y=B0+B1X+B2X2+εY = B _ { 0 } + B _ { 1 } X + B_ { 2 } X ^ { 2 } + \varepsilonY=B0​+B1​X+B2​X2+ε

A Certain Type of Rare Gem Serves as a Status $Y = B _ { 0 } + B _ { 1 } X + B_ { 2 } X ^ { 2 } + \varepsilon$