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).
Extracted text: 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). 13 34 52 28 50 25 y 2 6 5 9 3 Complete parts (a) through (e), given Ex = 202, Ey = 27, Ex? = 7938, Ey? = 159, Exy = 1071, and rx 0.7844. (a) Draw a scatter diagram displaying the data.
Extracted text: (b) Verify the given sums Ex, Ey, Ex?, Ey?, Exy, and the value of the sample correlation coefficient r. (Round your value forr to four decimal places.) Σχ Ey = Ex2 = Ey2 Σχy - r = (c) Find x, and y. Then find the equation of the least-squares line ý = a + bx. (Round your answers to four decimal places.) y = (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. y y y y a b C d : 10 10 10 10 5 5 5- 5 10 20 30 40 50 60 10 20 30 40 50 60 10 20 30 40 50 60 10 20 30 40 50 60 (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 2 to four decimal places. Round your answers for the percentages to two decimal place.) r2 = 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