Chapter 4.4, Problem 11PPS

(a)

To determine

To identify: the independent and the dependent variable, and make a scatter plot to determine the relationship, and to draw a line of fit for the scatter plot.

Explanation of Solution

Given information:

The time to the next eruption of Old faithful can be predicted by using the duration of the current eruption.

  

Calculation:

The independent variable is the duration of the eruptions and the dependent variable is the interval between eruptions.

Now, draw a line of fit for the scatter plot.

  

There is a positive correlation between the independent and dependent variables.

(b)

To determine

To write: the slope intercepts form of the equation for the line of fit, and to predict the interval after a 7.5 minute eruption.

Answer to Problem 11PPS

The equation is $y=13.5x+28$ .

The interval is 129.25.

Explanation of Solution

Given information:

The time to the next eruption of Old faithful can be predicted by using the duration of the current eruption.

  

Let $x$ represent the duration of the previous interval and let $y$ represent the time between eruptions.

Calculation:

As per the graph, sample answer using purpose taken two point $\left(2,55\right)$ and $\left(4,82\right)$ :

Now, calculation the slope,

  $\begin{array}{l}m=\frac{y_2-y_2}{x_2-x_1}\\ m=\frac{82-55}{4-2}\\ m=\frac{27}{2}\\ m=13.5\end{array}$

Then, use the slope and either of the two points, to find the $y$ intercept,

  $\begin{array}{c}y=mx+b\\ 82=13.5\left(4\right)+b\\ b=28\end{array}$

So, the equation is $y=13.5x+28$ .

Now, to find the interval after an equation of 7.5 minutes

So, $x=7.5$

Putting the value of $x$ in the equation, and get

  $\begin{array}{c}y=13.5x+28\\ =13.5\left(7.5\right)+28\\ =101.25+28\\ =129.25\end{array}$

So, the interval is 129.25.

(c)

To determine

To predict: the duration of the next eruption, and whether the equation be a useful model.

Answer to Problem 11PPS

The needy variable can be anticipated by the length of the emission.

Explanation of Solution

Given information:

The time to the next eruption of Old faithful can be predicted by using the duration of the current eruption.

  

Let $x$ represent the duration of the previous interval and let $y$ represent the time between eruptions.

Calculation:

The term of an emission is the autonomous variable and consequently isn't reliant on the past span. Just the span, the needy variable can be anticipated by the length of the emission.