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 13 30 50 28 50 25 y2 36 5 9 3 LAUSE SALT Complete parts (a) through (e), given Ex 196, y = 28, Ex2 7478, Ey2 164, Exy 1081, and r- 0.8786. (a) Draw a scatter diagram displaying the data. 33 30 x(total number of jobs (in hundreds x(total number of jobs (in hundreds x(total number of jobs in hundreds @ x(total number of jobs (in hundreds @º

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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).
x
13
30 50 28 50 25
y
2
3
5 9 3
USE SALT
Complete parts (a) through (e), given Ex= 196, y = 28, Ex2 = 7478, Ey2 = 164, Exy = 1081, and r = 0.8786.
(a) Draw a scatter diagram displaying the data.
15
15
x (total number of jobs (in hundreds))
x (total number of jobs (in hundreds))
x(total number of jobs (in hundreds)
x(total number of jobs (in hundreds))
(b) Verify the given sums Ex, Ey, Ex2, Ey2, Exy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.)
Ey2 =
(c) Find x, and y. Then find the equation of the least-squares lineŷ= a + bx. (Round your answers to four decimal places.)
Transcribed Image Text: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 13 30 50 28 50 25 y 2 3 5 9 3 USE SALT Complete parts (a) through (e), given Ex= 196, y = 28, Ex2 = 7478, Ey2 = 164, Exy = 1081, and r = 0.8786. (a) Draw a scatter diagram displaying the data. 15 15 x (total number of jobs (in hundreds)) x (total number of jobs (in hundreds)) x(total number of jobs (in hundreds) x(total number of jobs (in hundreds)) (b) Verify the given sums Ex, Ey, Ex2, Ey2, Exy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Ey2 = (c) Find x, and y. Then find the equation of the least-squares lineŷ= a + bx. (Round your answers to four decimal places.)
(d) Graph the least-squares line. Be sure to plot the point y) as a point on the line.
40
33
50
13
13
x (total number of jobs (in hundreds))
Ⓡ
x (total number of jobs (in hundreds))
x(total number of jobs (in hundreds))
x(total number of jobs (in hundreds))
(e) Find the value of the coefficient of determination 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 2 to four decimal places.
Round your answers for the percentages to two decimal place.)
2=
%
explained
unexplained
(f) For a neighborhood with x = 39 hundred jobs, how many are predicted to be entry level jobs? (Round your answer to two decimal places.)
hundred jobs
Transcribed Image Text:(d) Graph the least-squares line. Be sure to plot the point y) as a point on the line. 40 33 50 13 13 x (total number of jobs (in hundreds)) Ⓡ x (total number of jobs (in hundreds)) x(total number of jobs (in hundreds)) x(total number of jobs (in hundreds)) (e) Find the value of the coefficient of determination 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 2 to four decimal places. Round your answers for the percentages to two decimal place.) 2= % explained unexplained (f) For a neighborhood with x = 39 hundred jobs, how many are predicted to be entry level jobs? (Round your answer to two decimal places.) hundred jobs
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