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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. The researcher set up four large circular pens on sandy ocean bottoms off the coast of southern California. He chose young perch at random from a large group and placed 10,20,40 and60 perch in the four pens. Then he dropped the nets protecting the pens, allowing the bass to swarm in, and counted the perch left after two hours. Here are data on the proportions of perch eaten in four repetitions of this setup .

The explanatory variable is the number of perch (the prey) in a confined area. The response variable is the proportion of perch killed by bass (the predator) in two hours when the bass are allowed access to the perch. A scatterplot of the data shows a linear relationship.

We used Minitab software to carry out a least-squares regression analysis for these data. A residual plot and a histogram of the residuals are shown below. Check whether the conditions for performing inference about the regression model are met.

Step by step solution

01

Given Information

Need to find whether the conditions are satisfied are not.

02

Explanation

There are five conditions for regression inference are: Linear, Independent, Normal, Equal variance, Random

Linear: Satisfied, because all points in the residual plot are centered about 0.

Independent: Satisfied, because the subjects were randomly selected from a large population.

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

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

Random: Satisfied, because the subject was randomly selected from a large population.

Thus all conditions have been satisfied.

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