Let x be per capita income in thousands of dollars. Let y be the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information about x and y (Based on information from The Rating Guide to Life in America€™s Small Cities by G. S. Thomas, Prometheus Books):

Complete parts (a) through (e), given ˆ‘x = 53, ˆ‘y = 83.7, ˆ‘x2 = 471.04, ˆ‘y2 = 1276.83, ˆ‘xy = 755.89, and r ‰ˆ 0.934.
(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) Suppose a small city in Oregon has a per capita income of $10,000. What is the predicted number of MDs per 10,000 residents?

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