Chapter 12.2, Problem 34E

(a)

To determine

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

Explanation of Solution

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

  

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

Direction: Negative, because the scatterplot slopes upwards.

Form: Curved, because the points do not lie on a straight line.

Strength: Strong, because all points lie very close together in the same pattern.

Thus, this is the conclusion.

(b)

To determine

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

Answer to Problem 34E

The used transformation is the reciprocal of the volume.

Explanation of Solution

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

  $\begin{array}{l}P=k\times \frac{1}{V}\\ \text{Or, }\frac{1}{P}=\frac{1}{k}\times V\end{array}$

Thus, we note that the values on the horizontal axis are different from the value in the table for volume while the values on the vertical axis are the same values in the table for pressure. This then implies that the explanatory variable on the horizontal axis is the reciprocal of the volume and the response variable on the vertical axis is the pressure.

(c)

To determine

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

Answer to Problem 34E

The used transformation is the reciprocal of the pressure.

Explanation of Solution

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

  $\begin{array}{l}P=k\times \frac{1}{V}\\ \text{Or, }\frac{1}{P}=\frac{1}{k}\times V\end{array}$

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