Question

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 ?x=72, ?y=589, ?x^2=1340, ?y^2=72,277,?xy=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 show all steps and work please for credit

Answer 1

Note : Allowed to solve only 4 sub question in one post. (solved from a to e)

a) draw a scatter diagram for the data and the regression line

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?

Coefficient of determination(rsqaure) = 0.8588
It is the measure of the amount of varaiblity in y explained by x. Its value lies between 0 and 1. Greater the value, better is the model. In this case, it 85.88%, hence the model is good

d) Test the claim that the population correlation coefficient p is not zero at the 1% level of significance

Hence there is sufficient evidence to 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)​​​​​​​