MATHEMATICS

20. The logarithm transformation can be used

[removed]A) to overcome violations of the homoscedasticity assumption.
[removed]B) to test for possible violations of the homoscedasticity assumption.
[removed]C) to overcome violations of the autocorrelation assumption.
[removed]D) to test for possible violations of the autocorrelation assumption.

21. Which of the following is NOT used to determine observations that have an influential effect on the fitted model?

[removed]A) the hat matrix elements hi
[removed]B) the Cp statistic
[removed]C) the Studentized deleted residuals ti
[removed]D) Cook’s distance statistic

22. TABLE 15-2

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 hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they will gain by 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:

SUMMARY OUTPUT

ANOVA

Referring to Table 15-2, what is the value of the test statistic for testing whether there is an upward curvature in the response curve relating the demand (Y) and the price (X)?

[removed]A) -5.14
[removed]B) 373
[removed]C) 0.95
[removed]D) none of the above

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