15-3 A certain type of rare gem prices, the de as a that when the gem is status

Question

15-3 A certain type of rare gem prices, the de as a that when the gem is status symbol for many of its owners. In for low demand for eve valued at very of m theory, the they gain in high prices, However, by its on the the demand increases price due to the status where Y-demand Gn price is quadratic the model proposed to best explain the the Thus, s model thousands) model carat. was fit to and X retail price per data computer analysis obtained sample of 12 rare gems of this type. A portion of the SUMMARY from Microsoft Excel is shown below: OUTPUT Regression Statistics Multiple R 0.994 R Square 0.988 Standard Error 12.42 Observations 12 ANOVA Signif F SS MS 115145 57573 373 0.0001 Residual 1388 Total 116533 value Std Error t Stat Intercept 0.0001 286.42 29.64 0.0006 5.14 0.31 0.06 0.3647 Price Sq 0.000067 0.00007 0.95 48. Referring to Table 15-3, the value of the statistic for testing whether there is an upward curvature in the response curve relating the demand and the price a) -5.14 0.95 c) 373 d) None of the above. ANSWER: B TYPE: MC DIFFICULTY: Easy KEYWORDS: quadratic regression, t test on slope, test statistic 20

Explanation / Answer

In problem 48. it is asking for testing whether there is an upword curvature in the response curve relating to the demand (Y) and the price (X), since it is not asking for upword trend or any linear relationship, so from the table 15-3 the test statistic value for price sq given in answer B: 0.95 is correct.

49. In this question it is asking for the p-value for testing whether there is an upword curvature in the response curve relating to the demand (Y) and the price (X), so from table p-value corresponding to price sq is 0.3647 given in option C

50. The correct intepretation for coeffiient of determination is given by option B.
98.8% of the total variation in demand can be explained by the quadratic relationship between demand and price
Since the regression output here shown is quadratic regression, not the linear one.

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