Chapter 3.2, Problem 45E

(a)

To determine

To explain how do the regression line compare.

Explanation of Solution

It is given that:

  $\begin{array}{l}\widehat{y}=-115+5.13x\\ \widehat{y}=-297+6.41x\end{array}$

Thus, in the scatterplot given, we note that the two regressions lines are nearly parallel. This is confirmed by the equations of the regression lines, because $5.13\text{ and 6}\text{.41}$ are very close together. However, we note that the intercepts are very different because the constants $-115\text{ and }-\text{297}$ strongly differ in the equations of the regression lines. This is also noticeable in the scatterplot because the regression line for the athletes of the shotput, hammer throw and discus throw lies above the other regression line.

(b)

To determine

To find out how much more do you expect a $72$ inch discus thrower to weigh than a $72$ inch sprinter.

Answer to Problem 45E

  $72$ inch discus thrower to weigh $89.84$ pounds more than $72$ inch sprinter.

Explanation of Solution

It is given that:

  $\begin{array}{l}\widehat{y}=-115+5.13x\\ \widehat{y}=-297+6.41x\end{array}$

Thus, the weight of a $72$ inch discus thrower is calculated as:

  $\begin{array}{l}\widehat{y}=-115+5.13x\\ =-115+5.13(72)\\ =254.36\end{array}$

And the weight of a $72$ inch sprinter is calculated as:

  $\begin{array}{l}\widehat{y}=-297+6.41x\\ =-297+6.41(72)\\ =164.52\end{array}$

Thus, the difference between the two predicted values is:

  $\begin{array}{l}=254.36-164.52\\ =89.84\end{array}$

This then implies that we expect $72$ inch discus thrower to weigh $89.84$ pounds more than $72$ inch sprinter.