Question

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

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

Step-by-step solution

Given information

The given data is

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.