An economist is studying the job market in Denver area neighborhoods. Letx represent the total number of jobs in a given neighborhood, and lety represent the number of entry-level jobs in the same neighborhood. A sample of six Denver neighborhoods gave the following information (units in hundreds of jobs).
(a) Draw a scatter diagram displaying the data.
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(b) Verify the given sums Σ
x, Σ
y, Σ
x2, Σ
y2, Σ
xy, and the value of the sample correlation coefficient
r. (Round your value for
r to three decimal places.)
Σx = |
|
Σy = |
|
Σx
2 = |
|
Σy
2 = |
|
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.)
(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.)
r
2 = |
|
explained |
% |
unexplained |
% |
(f) For a neighborhood with
x = 42 hundred jobs, how many are predicted to be entry level jobs? (Round your answer to two decimal places.)
hundred jobs