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.

x 8.7 9.5 10.5 8.0 8.3 8.7

y 9.4 18.8 21.0 10.2 11.4 13.1

Complete parts (a) through (e), given x = 53.7, y = 83.9, x2 = 484.77, y2 = 1288.41, xy = 771.07, and r 0.922.

(b) Verify the given sums x, y, x2, y2, xy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

x =

y =

x2 =

y2 =

xy =

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

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(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) Suppose a small city in Oregon has a per capita income of 9.5 thousand dollars. What is the predicted number of M.D.s per 10,000 residents? (Round your answer to two decimal places.)

M.D.s per 10,000 residents