Chapter 12.2, Problem 33E

(a)

To determine

To make a reasonable accurate scatterplot of the data using length as the explanatory variable and describe what you see.

Explanation of Solution

The scatterplot of the following data given in the question taking length as the explanatory variable is as follows:

  

Thus, by looking at the scatterplot we can say that,

Direction: Positive, because the scatterplot slopes upwards.

Form: Curved, because the point in the upper right corner deviates from the general linear pattern.

Strength: Strong, because all points (except for one) lie very close together.

We also note an outlier in the upper right corner.

(b)

To determine

To identify the transformation that was used to linearize the curved pattern in part (a).

Answer to Problem 33E

The used transformation is the square root.

Explanation of Solution

The plot is given in the question for part (b) and also it is given that:

  $\text{Period}=\frac{2x}{\sqrt{g}}\sqrt{\text{length}}$

This then means that the explanatory variable on the horizontal axis is the square root of the length and the response variable on the vertical axis is the period. And this implies that the used transformation is the square root.

(c)

To determine

To identify the transformation that was used to linearize the curved pattern in part (a).

Answer to Problem 33E

The used transformation is the square.

Explanation of Solution

The plot is given in the question for part (c) and also it is given that:

  $\begin{array}{l}\text{Period}=\frac{2x}{\sqrt{g}}\sqrt{\text{length}}\\ \Rightarrow {\text{Period}}^2=\frac{{(2x)}^2}{g}\text{Length}\end{array}$

Thus, we note that the values on the horizontal axis are the same as the values for the length while the values on the vertical axis are higher than the values for the period given in the table. This then means that the explanatory variable on the horizontal axis is the length and the response variable on the vertical axis is the square of the period. This then implies that the used transformation is the square.