Chapter PII, Problem 18RE

(a)

To determine

To explain do the associations between the sizes of the heads and bodies of the two species appear to be strong.

Answer to Problem 18RE

Yes, the associations between the sizes of the heads and bodies of the two species appear to be strong.

Explanation of Solution

It is given in the question that the ranges inhabited by the Indian gharial crocodile and the Australian saltwater crocodile overlap in Bangladesh. The regression analysis for both is also given:

  $\begin{array}{l}\text{Indian Crocodile:}\\ \text{Intercept}=-69.3693\\ \text{IHead}=7.40004\\ R^2=97.2\%\end{array}$

  $\begin{array}{l}\text{Australian Crocodile:}\\ \text{Intercept}=-20.2245\\ \text{AHead}=7.71726\\ R^2=98\%\end{array}$

Thus, we can say that the associations between the sizes of the heads and bodies of the two species appear to be strong because the Indian crocodile R -squared and the Australian crocodile R -squared are both high which indicates strong variability between variables thus strong association.

(b)

To determine

To explain in what ways are the two relationships similar.

Explanation of Solution

It is given in the question that the ranges inhabited by the Indian gharial crocodile and the Australian saltwater crocodile overlap in Bangladesh. The regression analysis for both is also given:

  $\begin{array}{l}\text{Indian Crocodile:}\\ \text{Intercept}=-69.3693\\ \text{IHead}=7.40004\\ R^2=97.2\%\end{array}$

  $\begin{array}{l}\text{Australian Crocodile:}\\ \text{Intercept}=-20.2245\\ \text{AHead}=7.71726\\ R^2=98\%\end{array}$

Thus, the ways in which the two relationships are similar are that they both have close correlation as they have close R -squared and the slope are also very close.

(c)

To determine

To explain what is different about the two models and what does that means.

Explanation of Solution

It is given in the question that the ranges inhabited by the Indian gharial crocodile and the Australian saltwater crocodile overlap in Bangladesh. The regression analysis for both is also given:

  $\begin{array}{l}\text{Indian Crocodile:}\\ \text{Intercept}=-69.3693\\ \text{IHead}=7.40004\\ R^2=97.2\%\end{array}$

  $\begin{array}{l}\text{Australian Crocodile:}\\ \text{Intercept}=-20.2245\\ \text{AHead}=7.71726\\ R^2=98\%\end{array}$

Thus, by seeing the analysis for both the models we can say that the Indian crocodile has a much smaller intercept than the Australian crocodile so, this means that the Indian crocodile will have a shorter length.

(d)

To determine

To find out which species do you think it was and explain why.

Answer to Problem 18RE

It was Indian crocodile.

Explanation of Solution

It is given in the question that the ranges inhabited by the Indian gharial crocodile and the Australian saltwater crocodile overlap in Bangladesh. The regression analysis for both is also given:

  $\begin{array}{l}\text{Indian Crocodile:}\\ \text{Intercept}=-69.3693\\ \text{IHead}=7.40004\\ R^2=97.2\%\end{array}$

  $\begin{array}{l}\text{Australian Crocodile:}\\ \text{Intercept}=-20.2245\\ \text{AHead}=7.71726\\ R^2=98\%\end{array}$

For Indian crocodile:

  

For Australian crocodile:

  

So, the crocodile skeleton found had a head length of $62$ cm and a body length of $380$ cm, therefore, the species found is the Indian crocodile because the predicted length for the given head length is $389.43$ cm which is much closer than the predicted length of the Australian crocodile which was $458.25$ cm.