Chapter PII, Problem 9RE

(a)

To determine

To create a linear model of the association between Manatee deaths and powerboats registrations.

Answer to Problem 9RE

   .

Explanation of Solution

It is given in the question that marine biologists warn that the growing number of powerboats registered in Florida threatens the existence of manatees and the data is also given.Thus, we will select the data in the Excel and then go to the insert tab and create a scatterplot and then select the layout of the scatterplot with the regression line as:

  

Thus, the regression line will be as:

  

(b)

To determine

To interpret the slope of your model.

Explanation of Solution

It is given in the question that marine biologists warn that the growing number of powerboats registered in Florida threatens the existence of manatees and the data is also given. And the regression line is:

  

Thus, by the regression line we can interpret the slope of the model that for every $1000$ powerboats registered the manatees killed increases by $0.1315$ .

(c)

To determine

To interpret the y -intercept of your model.

Explanation of Solution

It is given in the question that marine biologists warn that the growing number of powerboats registered in Florida threatens the existence of manatees and the data is also given. And the regression line is:

  

Thus, by the regression line we can interpret the y -intercept of the model that the y -intercept of $-45.671$ does not make sense because that means with zero powerboat registration a negative number of manatees would die which is impossible.

(d)

To determine

To explain how accurately did your model predict the high number of manatee deaths in $2005$ .

Answer to Problem 9RE

The model overvalued deaths by $3.41$ .

Explanation of Solution

It is given in the question that marine biologists warn that the growing number of powerboats registered in Florida threatens the existence of manatees and the data is also given. And the regression line is:

  

Thus, the model predict the high number of manatee deaths in $2005$ as:

  

Thus, the model overvalued the manatees killed by:

  $\begin{array}{l}=82.41-79\\ =3.41\end{array}$

(e)

To determine

To explain which is better for the manatees, positive residuals or negative residuals.

Answer to Problem 9RE

Negative residual is better.

Explanation of Solution

It is given in the question that marine biologists warn that the growing number of powerboats registered in Florida threatens the existence of manatees and the data is also given. And the regression line is:

  

Thus, the negative residual is better because the negative residual will means less manatees died than were predicted to.

(f)

To determine

To explain what does your model suggest about the future for the manatee.

Explanation of Solution

It is given in the question that marine biologists warn that the growing number of powerboats registered in Florida threatens the existence of manatees and the data is also given. And the regression line is:

  

The model predicts about manatees deaths that manatees deaths will continue to increase but certain events could change that.