Chapter 9, Problem 10E

(a)

To determine

To interpret the slope and intercept of the model.

Answer to Problem 10E

For every year since $1970$ , there has, on average, been a decrease of about $\text{5}\text{.22924}$ nautical miles errors made and in the year $1970$ , there were $\text{292}\text{.089}$ nautical miles errors made.

Explanation of Solution

The scatterplot is given based on the $24-$ hour tracking errors made by the national hurricane centers in nautical miles over the years. And also it is given that:

  $\begin{array}{l}{R}^2=63\%\\ s=42.87\\ \text{Intercept =292}\text{.089}\\ \text{Years 1970 =-5}\text{.22924}\end{array}$

And the dependent variable is error. Now, we can say from the slope and intercept that for every year since $1970$ , there has, on average, been a decrease of about $\text{5}\text{.22924}$ nautical mileserrors made and in the year $1970$ , there were $\text{292}\text{.089}$ nautical miles errors made.

(b)

To determine

To interpret $s_e$ in this context.

Answer to Problem 10E

On average, the actual values fall within $42.87$ of the regression line.

Explanation of Solution

The scatterplot is given based on the $24-$ hour tracking errors made by the national hurricane centers in nautical miles over the years. And also it is given that:

  $\begin{array}{l}{R}^2=63\%\\ s=42.87\\ \text{Intercept =292}\text{.089}\\ \text{Years 1970 =-5}\text{.22924}\end{array}$

And the dependent variable is error. Now, $s_e$ in this context interprets that on average, the actual values fall within $42.87$ of the regression line. As $s_e$ is how far the actual data falls from the regression line.

(c)

To determine

To explain will they make it or not and why.

Answer to Problem 10E

Yes, they will make it.

Explanation of Solution

The scatterplot is given based on the $24-$ hour tracking errors made by the national hurricane centers in nautical miles over the years. And also it is given that:

  $\begin{array}{l}{R}^2=63\%\\ s=42.87\\ \text{Intercept =292}\text{.089}\\ \text{Years 1970 =-5}\text{.22924}\end{array}$

And the dependent variable is error. Now, the center has stated goal of achieving an average tracking error of $125$ nautical miles in $2009$ . Thus this goal can be made as $\begin{array}{l}\text{Predicted errors}=292.089-5.22924(\text{year since 1970})\\ =292.089-5.22924(39)\\ =86.1486<125\end{array}$

Which is less than $125$ thus, they can be able to make it.

(d)

To determine

To explain what if their goals were an average tracking error of $90$ nautical miles.

Answer to Problem 10E

Yes, they will make it.

Explanation of Solution

The scatterplot is given based on the $24-$ hour tracking errors made by the national hurricane centers in nautical miles over the years. And also it is given that:

  $\begin{array}{l}{R}^2=63\%\\ s=42.87\\ \text{Intercept =292}\text{.089}\\ \text{Years 1970 =-5}\text{.22924}\end{array}$

And the dependent variable is error. If their average tracking goals is $90$ nautical miles then it can also be done as,

  $\begin{array}{l}\text{Predicted errors}=292.089-5.22924(\text{year since 1970})\\ =292.089-5.22924(39)\\ =86.1486<90\end{array}$

Which is less than $90$ nautical miles hence it is true.

(e)

To determine

To explain what caution would you state about your conclusion.

Explanation of Solution

The scatterplot is given based on the $24-$ hour tracking errors made by the national hurricane centers in nautical miles over the years. And also it is given that:

  $\begin{array}{l}{R}^2=63\%\\ s=42.87\\ \text{Intercept =292}\text{.089}\\ \text{Years 1970 =-5}\text{.22924}\end{array}$

And the dependent variable is error. Thus, as we know that $2009$ could be beyond the scope of the linear model since the linear model only predicts up until $2005$ . Thus, we could be extrapolating about the conclusion.