The following data are based on information from the book The Rating Guide to Life in America€™s Small Cities (by G. S. Thomas, Prometheus Books). Let x be the percentage of 16- to 19-year-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, El Dorado, Hot Springs, Jonesboro, Rogers, and Russellville) reported the following information about x and y:

Complete parts (a) through (e), given ˆ‘x = 112.8, ˆ‘y = 32.4, ˆ‘x2 = 2167.14, ˆ‘y2 = 290.14, ˆ‘xy = 665.03, and r ‰ˆ 0.764.
(a) Draw a scatter diagram displaying the data.
(b) Verify the given sums ˆ‘x, ˆ‘y, ˆ‘x2, ˆ‘y2, and ˆ‘xy and the value of the sample correlation coefficient r.
(c) Find x, y, a, and b. Then find the equation of the least-squares line ŷ = α + bx.

(e) Find the value of the coefficient of determination r2. 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?
(f) If the percentage of 16- to 19-year-olds not in school and not graduates reaches 24% in a similar city, what is the predicted rate of violent crimes per 1,000 residents?

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