Chapter PII, Problem 8RE

(a)

To determine

To find out which is the explanatory variable.

Answer to Problem 8RE

The explanatory variable is the powerboat registrations.

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, as we know that the explanatory variable is that independent variable and response variable is that which is dependent variable. Thus, in this case the explanatory variable is the powerboat registrations because the scientists say that as it increase the number of manatees increases as well.

(b)

To determine

To make a scatterplot of these data and describe the association you see.

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, the scatterplot of powerboat registrations against manatees killed is as follows:

  

Thus, by looking at the scatterplot we can say that it has a positive correlation as the points are moving upward from left to right and the association between variable is fairly linear and moderately strong.

(c)

To determine

To find the correlation between Boat Registrations and Manatee Deaths.

Answer to Problem 8RE

  $r=0.946$ .

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 use excel to calculate the correlation between the variables.

Formula used:

  $=\text{CORREL}(\text{array1, array2})$

Calculation:

The correlation is calculated as:

Correlation=

=CORREL(Q18:Q40,R18:R40)

And the result will be as:

Correlation=

0.9461

(d)

To determine

To interpret the value of $R^2$ .

Answer to Problem 8RE

  $R^2=89.51\%$ .

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. Now, we calculate the $R^2$ ,

  $\begin{array}{l}{R}^2=r^2\\ \Rightarrow R^2={0.946}^2\\ \Rightarrow R^2=0.8951\\ \Rightarrow R^2=89.51\%\end{array}$

Thus, $89.51\%$ of variability in members killed is accounted for by powerboat registrations.

(e)

To determine

To explain does your analysis prove that powerboats are killing manatees.

Answer to Problem 8RE

No, it does not prove.

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 can say that the analysis does not prove that powerboats are killing manatees because the association does not prove causation.