An economist is studying the job market in Denver area neighborhoods. Let x represent the total number of jobs in a give

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An economist is studying the job market in Denver area
neighborhoods. Let x represent the total number
of jobs in a given neighborhood, and
let y 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).
Complete parts (a) through (e),
given Σx = 206, Σy = 29, Σx2 = 8058, Σy2 = 177, Σxy = 1165, and r ≈ 0.8889.
(a)
Draw a scatter diagram displaying the data.
A scatter diagram has a horizontal axis labeled
"x (total number of jobs (in hundreds))" with values
from 17 to 52 and a vertical axis labeled "y (number
of entry-level jobs (in hundreds))" with values from 2 to 9. The
scatter diagram has 6 points. A pattern goes down and right
becoming less steep from (17, 9) to (52, 2).
A scatter diagram has a horizontal axis labeled
"x (total number of jobs (in hundreds))" with values
from 2 to 9 and a vertical axis labeled "y (number of
entry-level jobs (in hundreds))" with values from 17 to 52. The
scatter diagram has 6 points. A pattern goes down and right
from (2, 52) to (9, 17).
A scatter diagram has a horizontal axis labeled
"x (total number of jobs (in hundreds))" with values
from 17 to 52 and a vertical axis labeled "y (number
of entry-level jobs (in hundreds))" with values from 2 to 9. The
scatter diagram has 6 points. A pattern goes up and right
from (17, 2) to (52, 9).
A scatter diagram has a horizontal axis labeled
"x (total number of jobs (in hundreds))" with values
from 2 to 9 and a vertical axis labeled "y (number of
entry-level jobs (in hundreds))" with values from 17 to 52. The
scatter diagram has 6 points. A pattern goes up and right
from (2, 17) to (9, 52).
(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 four decimal places.)
Σx=Σy=Σx2=Σy2=Σxy=r=
(c)
Find x, and y. Then find the
equation of the least-squares
line ŷ = a + bx.
(Round your answers to four decimal places.)
x=y=ŷ= + x
(d)
Graph the least-squares line. Be sure to plot the point
(x, y) as a point on the line.
A graph containing a trend line and a point has a horizontal
axis labeled "x (total number of
jobs (in hundreds))" with values from 2 to 9 and a vertical
axis labeled "y (number of entry‐level
jobs (in hundreds))" with values from 17 to 52. The trend line
enters the window in the first quadrant, goes up and right, passes
through the approximate point (2.4, 23), passes through
the approximate point (7.2, 45.1), and exits the window
in the first quadrant. The approximate point (4.8,
34.3) is plotted on the trend line.
A graph containing a trend line and a point has a horizontal
axis labeled "x (total number of
jobs (in hundreds))" with values from 17 to 52 and a vertical
axis labeled "y (number of entry‐level
jobs (in hundreds))" with values from 2 to 9. The trend line
enters the window in the first quadrant, goes up and right, passes
through the approximate point (17.3, 1.9), passes through
the approximate point (20, 2.4), passes through the
approximate point (48, 7.2), and exits the window in the
first quadrant. The approximate point (34.3, 4.8) is
plotted on the trend line.
A graph containing a trend line and a point has a horizontal
axis labeled "x (total number of
jobs (in hundreds))" with values from 2 to 9 and a vertical
axis labeled "y (number of entry‐level
jobs (in hundreds))" with values from 17 to 52. The trend line
enters the window in the first quadrant, goes down and right,
passes through the approximate point (2.5, 45.4), passes
through the approximate point (7.3, 22.7), and exits the
window in the first quadrant. The approximate point (4.8,
34.3) is plotted on the trend line.
A graph containing a trend line and a point has a horizontal
axis labeled "x (total number of
jobs (in hundreds))" with values from 17 to 52 and a vertical
axis labeled "y (number of entry‐level
jobs (in hundreds))" with values from 2 to 9. The trend line
enters the window in the first quadrant, goes down and right,
passes through the approximate point (20, 7.3), passes
through the approximate point (48, 2.5), and exits the
window in the first quadrant. The approximate point (34.3,
4.8) is plotted on the trend 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 four decimal places. Round
your answers for the percentages to two decimal place.)
r2=explained %unexplained %
(f)
For a neighborhood
with x = 33 hundred jobs, how many are
predicted to be entry level jobs? (Round your answer to two decimal
places.)
hundred jobs