Roadrunners Problem, Part 1: Naturalists place 30 roadrunners in a game preserve that

Chapter 8, Problem 5

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Roadrunners Problem, Part 1: Naturalists place 30 roadrunners in a game preserve that formerly had no roadrunners. Over the years, the population grows as shown in the table and in Figure 8-3l. a. Give a physical reason and a graphical reason why a logistic function would be a reasonable mathematical model for the roadrunner population as a function of time. By logistic regression, find the particular equation of the best-fitting logistic function. Plot the graph and the data on the same screen. Use a window with an x-range of 0 to 20 years. Sketch the result. b. What does your mathematical model predict for the roadrunner population at x = 20 years? What does the model predict for the maximum sustainable population? At approximately what value of x is the point of inflection, where the rate of population growth is a maximum? c. Find , the average of the y-values. Use to calculate SSdev, the sum of the squares of the deviations. Using the regression function in part a, calculate SSres, the sum of the squares of the residuals. Then find the coefficient of determination. How does this coefficient show that the logistic function fits the points quite well?