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

Exercise 27

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.
Education: Violent Crime The following data are based on information from the book Life in America's small cities (by G. S. Thomas, Prometheus Books).
Let x be the percentage of 16- to 19-years-olds not in school and not high school graduates. Let y be the reported violent crimes per 1000 residents. Six small cities in Arkansas (Blytheville, EI Dorado, Hot Springs, Jonesboro, Rogers, and Russellville) reported the following information about x and y :

Complete parts (a) through (e), given x = 112.8, y = 32.4, x ² = 2167.14, y ² = 290.14, xy = 665.03, and r 0.764.
(f) If the percentage of 16- to 19-years-olds not in school and not graduates reaches 24% in a similar city, what is the predicted rate of violent crimes per 1000 residents