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).
x | 17 | 30 | 48 | 28 | 50 | 25 |
y | 3 | 4 | 7 | 5 | 9 | 3 |
Complete parts (a) through (e), given Σx = 198, Σy = 31, Σx^{2} = 7402, Σy^{2} = 189, Σxy = 1172, and r ≈ 0.942.
(a) Draw a scatter diagram displaying the data.
Selection Tool
Line
Ray
Segment
Circle
Vertical Parabola
Horizontal Parabola
Point
No Solution
Help
5
10
15
20
25
30
35
40
45
50
55
60
1
2
3
4
5
6
7
8
9
10
Clear Graph
Delete Layer
Fill
WebAssign Graphing Tool
Graph LayersToggle Open/Closed
(b) Verify the given sums Σx, Σy,
Σx^{2}, Σy^{2}, Σxy, 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.)
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
r^{2}. 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 r^{2}
to three decimal places. Round your answers for the percentages to
one decimal place.)
r^{2} = | |
explained | % |
unexplained | % |
(f) For a neighborhood with x = 41 hundred jobs, how many
are predicted to be entry level jobs? (Round your answer to two
decimal places.)
hundred jobs
a)
b)
ΣX = | 198.000 |
ΣY= | 31.000 |
ΣX2 = | 7402.000 |
ΣY2 = | 189.000 |
ΣXY = | 1172.000 |
r = | 0.942 |
c)
X̅=ΣX/n = | 33.00 |
Y̅=ΣY/n = | 5.17 |
ŷ = | -0.498+0.172x |
e)
coefficient of determination r2 = | 0.887 | ||
explained = | 88.7% | ||
unexplained= | 11.3% |
f)
predicted value =-0.498+0.172*41= | 6.55 |
Get Answers For Free
Most questions answered within 1 hours.