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: 8.4 9.2 10.4 8.0 8.3 8.7 y: 9.4 18.9 20.8 10.2 11.4 13.1 Complete parts (a) through (e), given Σx = 53, Σy = 83.8, Σx2 = 471.94, Σy2 = 1283.82, Σxy = 759.35, and r ≈ 0.924. (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 = 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 8.6 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 Answer all sections
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:
8.4
9.2
10.4
8.0
8.3
8.7
y:
9.4
18.9
20.8
10.2
11.4
13.1
Complete parts (a) through (e), given Σx = 53, Σy = 83.8, Σx2 = 471.94, Σy2 = 1283.82, Σxy = 759.35, and r ≈ 0.924.
(a) Draw a
(b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample
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=
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 8.6 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
Answer all sections
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