Chapter 12.1, Problem 3E

To determine

To check whether the conditions for performing inference about the regression model are met.

Answer to Problem 3E

All conditions are met.

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. Thus, as we know that there are five conditions for regression inference are: Linear, Independent, Normal, Equal variance, Random. Thus, we have,

Linear: It is satisfied, because all points in the residual plot are centered about zero.

Independent: It is satisfied, because the subjects were randomly selected from a large population.

Normal: It is satisfied, because the histogram is roughly bell-shaped.

Equal variance: It is satisfied, because the vertical spread of the points in the residual plot is about the same everywhere.

Random: It is satisfied, because the subjects were randomly selected from a large population.

Thus all conditions have been satisfied.