Question
In: Statistics and Probability
Let x be per capita income in thousands of dollars. Let y be the number of...
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 | 9.4 | 10.2 | 8.0 | 8.3 | 8.7 |
| y | 9.5 | 18.0 | 21.2 | 10.2 | 11.4 | 13.1 |
Complete parts (a) through (e), given Σx = 53.6, Σy = 83.4, Σx2 = 481.98, Σy2 = 1269.3, Σxy = 761.13, and r ≈ 0.864.
(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 |
(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 9.8
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
Solutions
orchestra answered 2 years agoRelated Solutions
Let x be per capita income in thousands of dollars. Let y be the number of...
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 8.6 9.7 10.3
8.0 8.3 8.7 y 9.7 19.0 22.0 10.2 11.4 13.1 Complete parts (a)
through (e), given Σx = 53.6, Σy = 85.4, Σx2 = 482.72, Σy2 =
1344.7, Σxy = 784.51, and r ≈ 0.963.
(b) Verify the given sums Σx, Σy,...
Let x be per capita income in thousands of dollars. Let y be the number of...
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 9.1 9.8
8.0 8.3 8.7 y 9.8 18.4 21.2 10.2 11.4 13.1 Complete parts (a)
through (e), given Σx = 52.3, Σy = 84.1, Σx2 = 457.99, Σy2 =
1289.65, Σxy = 747.71, and r ≈ 0.958. (a) Draw a scatter diagram
displaying the...
Let x be per capita income in thousands of dollars. Let y be the number of...
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 8.3 9.3 10.2
8.0 8.3 8.7 y 9.9 18.1 20.6 10.2 11.4 13.1 Complete parts (a)
through (e), given Σx = 52.8, Σy = 83.3, Σx2 = 468, Σy2 = 1255.59,
Σxy = 750.81, and r ≈ 0.974. (a) Draw a scatter diagram displaying
the...
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