Question

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 14 31 49 28 50 25 y 1 3 7 5 9 3 Complete parts

(a) through (e), given: Σx = 197,Σy = 28 ,Σx2 = 7467 ,Σy2 = 174 ,Σxy = 1115 and r ≈ 0.941

(b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

Σx = Σy = Σx2 = Σy2 = Σxy = r =

(c) Find x, and y. Then find the equation of the least-squares line y hat = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

x =

y =

y hat= ( )+( )x

(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 r2 to three decimal places. Round your answers for the percentages to one decimal place.)

r2 =

explained %=

unexplained %=

(f) For a neighborhood with x = 34 hundred jobs, how many are predicted to be entry level jobs? (Round your answer to two decimal places.)

( )hundred jobs

Answer 1