Chapter 4, Problem 9CR

In Problems 9-14,

(a) Draw a scatter diagram for the data.

(b) Find $\bar{x},\bar{y},b$, and the equations of the least-squares line. Plot the line on the scatter diagram of part (a).

(c) Find the sample correlation coefficient r and the coefficient of determination $r^2$. What percentage of variation in y is explained by the least-squares model?

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 die. A random sample of Arizona bighorn sheep gave the following information:

x	1	2	3	4	5
y	14	18.9	14.4	19.6	20.0

Complete parts (a) through (c). given

${\displaystyle \sum x}=15;{\displaystyle \sum y}=86.9;{\displaystyle \sum x^2}=55;{\displaystyle \sum y^2}=1544.73;{\displaystyle \sum xy}=\mathrm{273.4.}$