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 9.0 9.0 9.8 8.0 8.3 8.7
y 9.8 18.3 20.6 10.2 11.4 13.1
Complete parts (a) through (e), given Σx = 52.8, Σy = 83.4, Σx2 = 466.62, Σy2 = 1260.9, Σxy = 744.97, and r ≈ 0.779.
(a) Draw a scatter diagram displaying the data.

(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 ^ = 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 ^ =  ——- +———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 9.4 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

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