Desert Ecology: Wildlife Bighorn sheep are beautiful wild

Chapter , Problem 5

(choose chapter or problem)

Desert Ecology: Wildlife Bighorn sheep are beautiful wild animals found throughout the western United States. Data for this problem are based on information taken from The Desert Bighorn, edited by Monson and Sumner (University of Arizona Press). Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information:

\(\Sigma x=15 ; \Sigma y=86.9 ; \Sigma x^{2}=55 ; \Sigma y^{2}=1544.73 ; \Sigma x y=273.4\)

(a) Draw a scatter diagram.

(b) Find the equation of the least-squares line.

(c) Find r. Find the coefficient of determination \(r^2\). Explain what these measures mean in the context of the problem.

(d) Test the claim that the population correlation coefficient is positive at the 1% level of significance.

(e) Given the lack of significance of r, is it practical to find estimates of y for a given x value based on the least-squares line model? Explain.