Let x be a random variable representing percentage change in neighborhood population in the past few 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:
x 29 2 11 17 7 6
y 173 35 132 127 69 53
Σx=72, Σy=589, Σx^2=1340, Σy^2=72,277,Σxy=9499
a) draw a scatter diagram for the data
b) find x bar, y bar, b and the equation 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. What percentage of the variation in y is explained by the least-squares model?
d) Test the claim that the population correlation coefficient p is not zero at the 1% level of significance.
e) For a neighborhood with x= 12% change in population in the past few years, predict the change in the crime rate (per 1000 residents)
f) verify that Se= 22.5908
g) Find a 80% confidence interval for the change in crime rate when the percentage change in population is x= 12%
h) Test the claim that the slope B of the population least-squares line is not zero at the 1% level of significance.
I) Find an 80% confidence interval for B and interpret its meaning