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Chapter 12: Q. 2 (page 796)

Students in a statistics class drew circles of varying diameters and counted how many Cheerios could be placed in the circle. The scatterplot shows the results.

The students want to determine an appropriate equation for the relationship between diameter and the number of Cheerios. The students decide to transform the data to make it appear more linear before computing a least-squares regression line. Which of the following single transformations would be reasonable for them to try?

I. Take the square root of the number of Cheerios.

II. Cube the number of Cheerios.

III. Take the log of the number of Cheerios.

IV. Take the log of the diameter.

(a) I and II

(b) I and III

(c) II and III

(d) II and IV

(e) I and IV

Short Answer

Expert verified

The single transformation that is reasonable for them to try is option (b) I and III.

Step by step solution

01

Given information

The given data is

02

Explanation

The scatterplot pattern suggests that a power model might be appropriate.

A power model uses the response variable's root or logarithm.

Cheerios is the response variable, thus we should try transformations I and III.

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Most popular questions from this chapter

Following the debut of the new SAT Writing test in March 2005, Dr. Les Perelman from the Massachusetts Institute of Technology collected data from a set of sample essays provided by the College Board. A least-squares regression analysis was performed on these data. The two graphs below display the results of that analysis. Explain why the conditions for performing inference are not met in this setting.

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Random assignment is part of a well-designed comparative experiment because

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Foresters are interested in predicting the amount of usable lumber they can harvest from various tree species. They collect data on the diameter at breast height (DBH) in inches and the yield in board feet of a random sample of 20Ponderosa pine trees that have been harvested. (Note that a board foot is defined as a piece of lumber 12inches by 12inches by 1inch.) A scatterplot of the data is shown below

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