? Let x represent percent change in the rate of violent crime and y represent percent change in the rate of imprisonment in the general U.S. population. For 7 recent years, the following data have been obtained. x 6.1 5.4 3.7 5.2 6.2 6.5 11.1 -1.1 -4.5 - 6.2 -4.0 3.6 -0.1 -4.4 LA USE SALT Complete parts (a) through (e), given Ex = 44.2, Zy = -16.7, Ex2 = 311, Zy2 = 108.23, Exy = -101.92, and r ~ 0.0755. (a) Draw a scatter diagram displaying the data. 11 10 N 00 y (percent change in the rate of imprisonment) y (percent change in the rate of imprisonment) -2 -4 0 2 4 5 6 7 8 9 10 11 - 6 -4 -2 x (percent change in the rate of violent crime) O x (percent change in the rate of violent crime) O 4 11/ N 10 O y (percent change in the rate of imprisonment) 00 - 2 (percent change in the rate of imprisonment) . . -4 -6 5 6 7 8 9 10 11 4: (b) Verify the given sums Ex, Ey, Ex, Ey", Exy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Ex = Zy = Ex2 = Ey? = Exy = r = (c) Find x, and y. Then find the equation of the least-squares line y = a + bx. (Round your answer to four decimal places.) * = y = V = (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. 4 4 N 2 - 0 y (percent change in the rate of imprisonment) y (percent change in the rate of imprisonment) - 21 -2 -4 -4 -6 -6 11 4 5 8 9 10 10 11 5 8 9 4 x (percent change in the rate of violent crime) O x (percent change in the rate of violent crime) O 10 10 change in the rate of imprisonment) Change in the rate of imprisonment) 8 8 6 6(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. 4 4 21 y (percent change in the rate of imprisonment) y (percent change in the rate of imprisonment) - 21 -4 -6 4 5 7 8 10 11 4 5 8 9 10 11 O x (percent change in the rate of violent crime) O x (percent change in the rate of violent crime) 10 10 8 00 y (percent change in the rate of imprisonment) y (percent change in the rate of imprisonment) 6 4 - 6 -4 -2 2 - 6 -2 2 x (percent change in the rate of violent crime) O x (percent change in the rate of violent crime) O (e) Find the value of the coefficient of determination . 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.) 2 = explained % unexplained10 8 8 y (percent change in the rate of im 6 y (percent change in the rate of imp 6 4 4 - 6 -4 - 2 2 -4 -2 0 2 O x (percent change in the rate of violent crime) O x (percent change in the rate of violent crime) (e) Find the value of the coefficient of determination . 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 2 to four decimal places. Round your answers for the percentages to two decimal place.) 2 =1 explained % unexplained (f) Considering the values of r and r, does it make sense to use the least-squares line for prediction? Explain your answer. The correlation between the variables is so high that it makes sense to use the least-squares line for prediction. The correlation between the variables is so low that it does not make sense to use the least-squares line for prediction. The correlation between the variables is so low that it makes sense to use the least-squares line for prediction. The correlation between the variables is so high that it does not make sense to use the least-squares line for prediction