Chapter 8, Problem 22E

(a)

To determine

To explain what the slope of the line says about how long a roller coaster ride may last and the height of the coaster.

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 $R^2=12.4\%$ . And the regression analysis gives the model:

  $\text{<mover accent="true"><mo>D</mo><mo>^</mo></mover> uration}=91.033+0.242\text{Drop}$

Thus, the slope of the line says about how long a roller coaster ride may last and the height of the coaster is that there is an increase of about $0.242$ feet for every $91.033$ seconds.

(b)

To determine

To explain how long would you predict the rides last.

Answer to Problem 22E

The duration of the ride is $139.433$ seconds.

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 $R^2=12.4\%$ . And the regression analysis gives the model:

  $\text{<mover accent="true"><mo>D</mo><mo>^</mo></mover> uration}=91.033+0.242\text{Drop}$

It is given that a new roller coaster advertises an initial drop of $200$ feet. Thus, the duration of the ride is:

  $\begin{array}{l}\text{<mover accent="true"><mo>D</mo><mo>^</mo></mover> uration}=91.033+0.242\text{Drop}\\ =91.033+0.242\times 200\\ =139.433\end{array}$

Thus, the duration of the ride is $139.433$ seconds.

(c)

To determine

To explain is this longer or shorter than you had expect and by how much and what is that called.

Answer to Problem 22E

It is longer than expected.

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 $R^2=12.4\%$ . And the regression analysis gives the model:

  $\text{<mover accent="true"><mo>D</mo><mo>^</mo></mover> uration}=91.033+0.242\text{Drop}$

And it is given another coaster with a $150$ -foot initial drop advertises a two-minute ride. Thus, the duration of the ride is:

  $\begin{array}{l}\text{<mover accent="true"><mo>D</mo><mo>^</mo></mover> uration}=91.033+0.242\text{Drop}\\ =91.033+0.242\times 150\\ =127.333\end{array}$

Thus, this is longer than we had expected. This can be explained as:

  $\begin{array}{l}\text{Difference}=127.333-120\\ =7.333\text{ seconds}\end{array}$

And this called the predicted value for the duration of the ride of the roller coaster.