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. x 24.2 18.6 17.8 14.9 19.0 17.5 y 13.0 4.6 8.8 1.3 0.8 3.6 Complete parts (a) through (e), given Σx = 112, Σy = 32.1, Σx2 = 2137.7, Σy2 = 282.89, Σxy = 654.37, and r ≈ 0.763. (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? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.) r2 = explained % unexplained % (f) If the percentage of 16- to 19-year-olds not in school and not graduates reaches 22.5% in a similar city, what is the predicted rate of violent crimes per 1000 residents? (Round your answer to two decimal places.) violent crimes per 1000 residents
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.
| x | 24.2 | 18.6 | 17.8 | 14.9 | 19.0 | 17.5 |
| y | 13.0 | 4.6 | 8.8 | 1.3 | 0.8 | 3.6 |
Complete parts (a) through (e), given Σx = 112, Σy = 32.1, Σx2 = 2137.7, Σy2 = 282.89, Σxy = 654.37, and r ≈ 0.763.
(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? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.)
| r2 = | |
| explained | % |
| unexplained | % |
(f) If the percentage of 16- to 19-year-olds not in school and not graduates reaches 22.5% in a similar city, what is the predicted rate of violent crimes per 1000 residents? (Round your answer to two decimal places.)
violent crimes per 1000 residents
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