6. [-/5.31 Points] DETAILS BBUNDERSTAT12 9.2.007.MI.S. MY NOTES ASK YOUR TEACHER An economist is studying the job market in Denver area neighborhoods. Let x represent the total number of jobs in a given neighborhood, and let y represent the number of entry-level jobs in the same neighborhood. A sample of six Denver neighborhoods gave the following information (units in hundreds of jobs). 15 30 50 25 1 2 7 5 LA USE SALT Complete parts (a) through (e), given Ex = 200, Zy = 27, Ex2 = 7738, Zy2 = 169, Exy = 1104, and r = 0.9043. (a) Draw a scatter diagram displaying the data. 8 y (number of entry-level jobs (in hundreds)) y (number of entry-level jobs (in hundreds) N 15 25 30 35 40 45 50 15 25 35 40 45 50 O x (total number of jobs (in hundreds)) DC x (total number of jobs (in hundreds)) y (number of entry-level jobs (in hundreds)) y (number of entry-level jobs (in hundreds)) 25 20 15 8 2 8 O x (total number of jobs (in hundreds)) (total number of jobs (in hundreds)) (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 = Ey Ey Exy = (c) Find x, and y. Then find the equation of the least-squares line y = a + bx. (Round your answers to four decimal places.) * = R =(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. 50 8 40 y (number of entry-level jobs (in hundreds)) y (number of entry-level jobs (in hundreds) 30 4 20 2 6 8 15 20 25 30 35 40 45 50 O x (total number of jobs (in hundreds)) x (total number of jobs (in hundreds)) 50 40 y (number of entry-level jobs (in hundreds)) y (number of entry-level jobs (in hundreds)) 30 4 20 LL N 8 15 20 25 30 35 40 45 50 O x (total number of jobs (in hundreds)) x (total number of jobs (in hundreds)) (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 / to four decimal places. Round your answers for the percentages to two decimal place.) 2 = explained % unexplained (f) For a neighborhood with x = 31 hundred jobs, how many are predicted to be entry level jobs? (Round your answer to two decimal places.) hundred jobs