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) X 17 30 52 28 50 25 2 5 9 3 In USE SALT Complete parts (a) through (e), given Ex = 202, Ey = 29, Ex2 = 7802, Ey? = 177, Exy = 1153, and r 2 0.9199. (a) Draw a scatter diagram displaying the data. 00 y (number of entry-level jobs (in hundreds)) y (number of entry-level jobs (in hundreds) N 20 25 30 35 40 45 50 20 25 30 35 40 45 50 O x (total number of jobs (in hundreds)) x (total number of jobs (in hundreds)) i 50 50 45 45 40 mber of entry-level jobs (in hundreds)) er of entry-level jobs (in hundreds)) 40 35 30 30 25 25 2050 35 y (number of entry-level jobs (in hundred y (number of entry-level jobs (in hundreds)) 30 25 25 20 20 2 3 4 5 6 8 9 2 3 4 5 6 7 8 9 O x (total number of jobs (in hundreds)) O x (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 = 202 Ey = 29 Ex2 = 33.6667 X Ey = 4.8333 X Exy = 1001.3333 X = 176.6667 X (c) Find x, and y. Then find the equation of the least-squares line y = a + bx. (Round your answers to four decimal places.) X = 0.1764 X y = -1.1065 X y = 0.17643 + -1.1065 X x (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. 50 y-level jobs (in hundreds)) -level jobs (in hundreds)) 45 3520 y (numbe y (number 2 3 4 5 8 9 20 25 30 35 40 45 50 O x (total number of jobs (in hundreds)) x (total number of jobs (in hundreds)) 50 00 y (number of entry-level jobs (in hundreds)) A U O Y y (number of entry-level jobs (in hundreds)) 20 N 2 3 6 7 8 9 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.) 12 = explained % unexplained % (f) For a neighborhood with x = 37 hundred jobs, how many are predicted to be entry level jobs? (Round your answer to two decimal places.) |hundred jobs