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 |
18 |
31 |
51 |
28 |
50 |
25 |
y |
1 |
4 |
7 |
5 |
9 |
3 |
Complete parts (a) through (e), given Σx = 203, Σy = 29, Σx^{2} = 7795, Σy^{2} = 181, Σxy = 1164, and r ≈ 0.940.
(a) Draw a scatter diagram displaying the data.
(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=Σx = |
||
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.)
(f) For a neighborhood with x = 30 hundred jobs, how
many are predicted to be entry-level jobs? (Round your answer to
two decimal places.)
hundred jobs
b)
Σx = 203,
Σy = 29,
Σx^{2} = 7795,
Σy^{2} = 181,
Σxy = 1164,
r ≈ 0.940
c)
xbar =33.83
ybar=4.83
yhat=-1.841+0.197x
e)
coefficient of determination r^{2} =0.883
explained % =88.3%
unexplained % =11.7%
f)
predicted value =-1.841+0.197*30=4.07 (try 4.08 if this comes wrong)
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