Chapter 9, Problem 28E

(a)

To determine

To explain what does “the value of $s_e$ is much smaller” means in this context.

Explanation of Solution

We see in the previous exercise that the swimmer Vicki Keith round trip swim of Lake Ontario was an outlier among the other one-way time trip. Here is the new regression after the unusual point is removed from the previous exercise. Thus, we have,

  $\begin{array}{l}{R}^2=4.1\%\\ s=292.6\\ \text{Intercept}=-11048.7\\ \text{Year}=6.17091\end{array}$

Thus, “the value of $s_e$ is much smaller” means in this context that a smaller $s_e$ means that the regression line is closer to the actual times. That is the error in the standard deviation is small so the observed values is closer to the actual values so does the regression line.

(b)

To determine

To explain would you be willing to say that the Lake Ontario swimmers are getting faster or slower.

Answer to Problem 28E

The Lake Ontario swimmers are getting faster.

Explanation of Solution

We see in the previous exercise that the swimmer Vicki Keith round trip swim of Lake Ontario was an outlier among the other one-way time trip. Here is the new regression after the unusual point is removed from the previous exercise. Thus, we have,

  $\begin{array}{l}{R}^2=4.1\%\\ s=292.6\\ \text{Intercept}=-11048.7\\ \text{Year}=6.17091\end{array}$

Thus, we can say that the Lake Ontario swimmers are getting faster since the slope of the regression line of this new regression calculated from removing the unusual point in the previous exercise is positive so, the swimmers will be faster as the outlier that is affecting the result is removed.