Chapter 12, Problem T12.2SPT

To determine

To find out which of the following transformation would be reasonable for them to try.

Answer to Problem T12.2SPT

Option (b) is the correct option.

Explanation of Solution

Students wanted to draw a circle and wanted to see how many cheerios can be fitted in the circle. To see the better result they transform the data to make it appear more linear before computing a linear regression line. Thus, we have to find out which of the following transformation would be reasonable for them to try. Thus, we have that we note that the pattern in the given scatterplot is similar to a quadratic function, which implies that a graph of the form $y=a{x}^2+b$ could be a possible model. However, this implies that the number of cheerios is the square of the diameter up to some constants and an appropriate transformation is then taking a square root of the number of cheerios. Thus, I is an appropriate transformation.

Similarly, we note that the pattern in the given scatterplot is also similar to an exponential function, therefore it could be possible model. However, this implies that the number of cheerios is the exponential of the diameter up to some constant and an appropriate transformation is then taking the logarithm of the number of cheerios. Thus, III is an appropriate transformation.

Thus, option (b) is the correct option.