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(3) 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 8.2 9.2 10.2 8 8.3 8.7 y 9.9 18.2 21 10.2 11.4 13.1
Complete parts (a) through (e), given Σx = 52.6, Σy = 83.8, Σx2 = 464.5, Σy2 = 1275.86, Σxy = 753.01, and r ≈ 0.974.
(a) Draw a scatter diagram displaying the data.

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(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  = 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 = = +  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 9.3 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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Step 1

Hi, since the problem posted by you contains multiple sub-parts, we are answering the first three subparts. If you need any specific sub-part to be answered, please submit that particular sub-pat or specify the subpart number in the message box.

Step 2

Part (a):

The scatter diagram displaying the data is as follows:

Step 3

Part (b):

Using calculator, the following preliminary calculations verified.

∑x = (8.2 + 9.2 + 10.2 + 8 + 8.3 + 8.7) = 52.6.

∑x2 = (8.2 2 + 9.22 + 10.22 + 82 + 8.32 + 8.72) = 464.5.

∑y = (9.9 + 18.2 + 21 + 10.2 + 11.4 + 13.1) = 83.8.

∑y2 = (9.92 + 18.2 2 + 212 + 10.22 + 11.42 + 13.12) = 1,275.86.

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