Understanding Basic Statistics 6th Edition by Charles Henry Brase,Corrinne Pellillo Brase

Exercise 24

Draw a scatter diagram displaying the data.
(b) Verify the given sums x , y , x 2 , y 2 , and xy , and the value of the sample correlation coefficient r.
(c) Find
, a , and b. Then find the equation of the least-squares line = a + bx.
(d) Graph the least-squares line on your scatter diagram. Be sure to use the point(
) as one of the points on the line.
(e) Interpretation Find the value of the coefficient of determination r 2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line What percentage is unexplained Answers may vary slightly due to rounding.
Violent Crimes: Prisons Dose prison really deter violent crime Let x represent percent change in the rate of violent crime and y represent percent change in the rate of imprisonment in the general U.S. population. For 7 recent years, the following data have been obtained (Source: The crime Drop in America , edited by Blumstein and wallman, Cambridge University Press).

Complete parts (a) through (e), given x = 44.7, y =-17.4, x ² = 315.85, y ² = 116.18, xy = 107.18, and r 0.084.
(f) Critical Thinking Considering the value of r and r 2 , does it make sense to use the least-squares line for application Explain.