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 (in hundreds of jobs):

Complete parts (a) through (e), given ˆ‘x = 202, ˆ‘y = 28, ˆ‘x2 = 7754, ˆ‘y2 = 164, ˆ‘xy = 1096, and r ‰ˆ 0.860.
(a) Draw a scatter diagram displaying the data.
(b) Verify the given sums ˆ‘x, ˆ‘y, ˆ‘x2, ˆ‘y2, and ˆ‘xy and the value of the sample correlation coefficient r.
(c) Find x, y, a, and b. Then find the equation of the least-squares line ŷ = α + bx.

(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?
(f) For a neighborhood with x = 40 (hundred) jobs, how many are predicted to be entry-level jobs?
(f) Suppose a car weighs x = 38 (hundred pounds). What does the least-squares line forecast for y 5 miles per gallon?

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