Chapter 8, Problem 20E

(a)

To determine

To find out what is the correlation between drop and duration and explain why you chose the sign $(+\text{ or }-)$ you did.

Answer to Problem 20E

The correlation between drop and duration is $-0.352$ .

Explanation of Solution

It is given in the question that, people who responded to a discovery channel poll named the ten best roller coasters in the United States. In previous exercise it shows the length of the initial drop and the duration of the ride. A regression to predict duration from drop has $R^2=12.4\%$ . Thus, the correlation between drop and duration is calculated as:

  $\begin{array}{l}{r}^2=R^2\\ \Rightarrow r^2=0.124\\ \Rightarrow r=\sqrt{0.124}\\ \Rightarrow r=-0.352\end{array}$

Thus, the correlation between drop and duration is $-0.352$ . In this, we use the $-$ sign because as drop increases, duration decreases since you would likely be going faster at the bottom.

(b)

To determine

To explain what would you predict about the duration of the ride on a coaster whose initial drop was $1$ standard deviation below the mean drop.

Explanation of Solution

It is given in the question that, people who responded to a discovery channel poll named the ten best roller coasters in the United States. In previous exercise it shows the length of the initial drop and the duration of the ride. A regression to predict duration from drop has $R^2=12.4\%$ . Thus, we predict about the duration of the ride on a coaster whose initial drop was $1$ standard deviation below the mean drop because the duration would be $0.35$ standard deviations above the mean. As,

  $\begin{array}{l}r=\frac{z_y}{z_x}\\ \Rightarrow -0.35=\frac{z_y}{-1}\\ \Rightarrow z_y=0.35\end{array}$

(c)

To determine

To explain what would you predict about the duration of the ride on a coaster whose initial drop was $3$ standard deviation above the mean drop.

Explanation of Solution

It is given in the question that, people who responded to a discovery channel poll named the ten best roller coasters in the United States. In previous exercise it shows the length of the initial drop and the duration of the ride. A regression to predict duration from drop has $R^2=12.4\%$ . Thus, we predict about the duration of the ride on a coaster whose initial drop was $3$ standard deviation above the mean drop because the duration would be $1.05$ standard deviations below the mean. As,

  $\begin{array}{l}r=\frac{z_y}{z_x}\\ \Rightarrow -0.35=\frac{z_y}{3}\\ \Rightarrow z_y=-1.05\end{array}$