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 y 19.0 17.5 13.0 4.6 9.1 1.3 0.8 3.6 In USE SALT Complete parts (a) through (e), given Ex = 113.2, Zy = 32.4, Ex2 = 2183.28, Zy = 288.26, Exy = 668.32, and r = 0.7769. (a) Draw a scatter diagram displaying the data. 24 12 22 10 8 20 y (violent crimes (per 1000 residents)) y (violent crimes (per 1000 residents)) 18 16 8 10 12 16 18 20 22 24 x (in percent) x (in percent) O 2 24 10 22 y (violent crimes (per 1000 residents)) 20 y (violent crimes (per 1000 residents)) 18 N 24 16 16 18 20 22 x (in percent) 12 6 8 10 O(b) Verify the given sums Ex, Ey, Ex2, Ey, Exy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Ex = 113.2 Ey = 32.4 Ex2 = 2183.3 X Ey2 = 288.3 X Exy = 668.3 X r = 0.604 X (c) Find x, and y. Then find the equation of the least-squares line y = a + bx. (Round your answer to four decimal places.) X = 18.9 X y = 5.4 y = 1.199 * + - 17.221 X x (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. 24 12 22 20 y (violent crimes (per 1000 residents) y (violent crimes (per 1000 residents)) 18 16 16 18 20 22 24 12 6 8 10 2 x (in percent) x (in percent) O O 12 24 10 00 22 plent crimes (per 1000 residents)) rimes (per 1000 residents)) 20 1822 10 20 00 y (violent crimes (per 1000 resident y (violent crimes (per 1000 residents 18 16 N 2 6 8 10 12 16 BT 20 22 24 O x (in percent) O x (in percent) 24 2 10 22 y (violent crimes (per 1000 residents)) 20 y (violent crimes (per 1000 residents)) 18 N 16 16 18 20 22 24 2 8 10 12 x (in percent) O O x (in percent) (e) Find the value of the coefficient of determination r. 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 r to four decimal places. Round your answers for the percentages to two decimal place.) 12 = 0.604 X 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 Need Help? MacBook Pro