Chapter 4, Problem 10CR

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?

Focus Problem: Changing Population and Crime Rate Let x be a random variable representing percentage change in neighborhood population in the past lew years, and let y be a random variable representing crime rate (crimes per 1000 population). A random sample of six Denver neighborhoods gave the following information (Source: Neighborhood Facts. The Piton Foundation).

X	29	2	11	17	7	6
y	173	35	132	127	69	53

Complete parts (a) through (c), given

${\displaystyle \sum x}=72;{\displaystyle \sum y}=589;{\displaystyle \sum x^2}=1340;{\displaystyle \sum y^2}=72.277;{\displaystyle \sum xy}=9499$

(d) For a neighborhood with x = 12 change in population in the past few years, predict the change in the crime rale (per 1000 residents).