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 24.3 19.2 18.3 14.9 19.0 17.5 y 13.0 4.6 9.1 1.3 0.8 3.6 Complete parts (a) through (e), given Σx = 113.2, Σy = 32.4, Σx2 = 2183.28, Σy2 = 288.26, Σxy = 668.32, and r ≈ 0.7769. (b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r = c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answer to four decimal places.) x = y = ^ y =__ +___x (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 four decimal places. Round your answers for the percentages to two 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 | 24.3 | 19.2 | 18.3 | 14.9 | 19.0 | 17.5 |
| y | 13.0 | 4.6 | 9.1 | 1.3 | 0.8 | 3.6 |
Complete parts (a) through (e), given Σx = 113.2, Σy = 32.4, Σx2 = 2183.28, Σy2 = 288.26, Σxy = 668.32, and r ≈ 0.7769.
(b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample
| Σx = | |
| Σy = | |
| Σx2 = | |
| Σy2 = | |
| Σxy = | |
| r = |
c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answer to four decimal places.)
| x | = | |
| y | = | |
|
^ y |
=__ | +___x |
(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 four decimal places. Round your answers for the percentages to two 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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