Chapter 12.1, Problem 5E

To determine

To explain what each parameter represents in context and then provide an estimate for each.

Answer to Problem 5E

  $\begin{array}{l}a=0.12049\\ b=0.008569\\ s=0.1886\end{array}$

Explanation of Solution

In the question, researchers examined the nature in which it regulates the size of animal predators which remove higher proportion of the population than when the density of the prey is low. The explanatory variable is the number of perch in a confined area and the response variable is the proportion of perch killed by bass in two hours when the bass are allowed access to the perch. The scatterplot is given and it shows a linear relationship. And the residual plot for least square regression line is given. The computer output is given for this data. $\alpha$ id the y -intercept which is also the estimate of the proportion of fish killed when the tank contains zero fish. The estimate of $\alpha$ is given in the column of “Coef” and in the row of “Constant”:

  $\alpha =0.12049$

  $\beta$ is the slope which means the estimate proportion of fish killed per fish present in the tank. The estimate of $\beta$ is given in the column of “Coef” and in the row of “Perch”:

  $b=0.008569$

  $\sigma$ is the standard deviation of the proportion of fish killed about the population regression line. The estimate of $\sigma$ is given is the output as S =:

  $s=0.1886$ .