Chapter 12: Q. 6 (page 788)

Prey attracts predators Here is one way in which nature regulates the size of animal populations: high population density attracts predators, which remove a higher proportion of the population than when the density of the prey is low. One study looked at kelp perch and their common predator, the kelp bass. On each of four occasions, the researcher set up four large circular pens on sandy ocean bottoms off the coast of southern California. He randomly assigned young perch to $1$ of $4$ pens so that one pen had $10$ perch, one pen had $20$ perch, one pen had $40$ perch, and the final pen had $60$ perch. Then he dropped the nets protecting the pens, allowing bass to swarm in, and counted the number of perch killed after two hours. A regression analysis was performed on the $16$ data points using x=number of perch in pen and y=proportion of perch killed. Here is a residual plot and a histogram of the residuals. Check whether the conditions for performing inference about the regression model are met.

Short Answer

Expert verified

Normal, equal standard deviation, random, independent, and linear are some of the requirements for regression inferences.

Step by step solution

Given information

We have to explain that whether the state for performing inference about the regression model are met or not.

Simplification

Normal,equalstandarddeviation,random,independent,andlineararesomeoftherequirementsforregressioninferences.

Normal: satisfied; the rationale for this is that the

16

young perch samples represented less than

10 %

of all young perches.

The reason for this is that the vertical distribution of dots in the residual figure is roughly the same everywhere, resulting in an equal standard deviation.

The explanation for this is that the individual was assigned to a pen at random. Because the sample of sixteen juvenile perches represents less than

10 %

of all young perches, independent: satisfied. Because there isn't enough significant curvature, linear is satisfied, and percent is the residual figure.

As a result, all states or requirements have been met.