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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

The body’s natural electrical field helps wounds heal. If diabetes changes this field, it might explain why people with diabetes heal more slowly. A study of this idea compared randomly selected normal mice and randomly selected mice bred to spontaneously develop diabetes. The investigators attached sensors to the right hip and front feet of the mice and measured the difference in electrical potential (in millivolts) between these locations. Graphs of the data for each group reveal no outliers or strong skewness. The computer output below provides numerical summaries of the data26.

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