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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).x153251285025y337593Complete parts (a) through (e), given Σx = 201, Σy = 30, Σx2 = 7759, Σy2 = 182, Σxy = 1163, and r ≈ 0.872.(a) Draw a scatter diagram displaying the data. Flash Player version 10 or higher is required for this question. You can get Flash Player free from Adobe's website. (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 three decimal places.)Σx = Σy = Σx2 = Σy2 = 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 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.)r2 = 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

Question

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 15 32 51 28 50 25
y 3 3 7 5 9 3

Complete parts (a) through (e), given Σx = 201, Σy = 30, Σx2 = 7759, Σy2 = 182, Σxy = 1163, and r ≈ 0.872.

(a) Draw a scatter diagram displaying the data.

 
Flash Player version 10 or higher is required for this question. 
You can get Flash Player free from Adobe's website.

 

(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 three decimal places.)
Σx =  
Σy =  
Σx2 =  
Σy2 =  
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 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.)
r2 =  
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
check_circleAnswer
Step 1

Scatter Plot

It is a Graph between two variables. It is plotted to check the relationship between the two variables.

Steps to plot Scatter Plot on Excel

  1. Enter the data in the excel sheet
  2. Go to insert and click scatter plot
  3. Scatter plot will be plotted 
K
H
F
D
C
B
A
X
3
15
10
3
32
7
9
51
8
9
50
7
3
25
6
5
4
3
2
1
0
60
50
40
20
10
0
30
T
LO.
28
help_outline

Image Transcriptionclose

K H F D C B A X 3 15 10 3 32 7 9 51 8 9 50 7 3 25 6 5 4 3 2 1 0 60 50 40 20 10 0 30 T LO. 28

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Step 2

Calculation of  correlation coefficient r

Σ-a
ΣΥ.
201
30
=
2
7759
Σε
182
Σ
υ-
xy = 1163
Formula for calculating the correlation coefficient is
6
T6
n
6
16
-6
Putting all the values in the equation
6 x 1163 201 x 30
r=
|(6 x 7759 2012)(6 x 182 - 302)
r = 0.872
help_outline

Image Transcriptionclose

Σ-a ΣΥ. 201 30 = 2 7759 Σε 182 Σ υ- xy = 1163 Formula for calculating the correlation coefficient is 6 T6 n 6 16 -6 Putting all the values in the equation 6 x 1163 201 x 30 r= |(6 x 7759 2012)(6 x 182 - 302) r = 0.872

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Step 3

Finding The equation of least square line

...

a y bx
Σx, Σν:
16
n i1XiVi
b =
2.
- (2*)
16
i=1
ΣΕ1
Li 1
Putting values, to calculate b first
6 x 1163 201 x 30
b
= 0.15407
6 x 7759 2012
Σν
30
5
6
n
Σχ
201
33.5
6
n
Calculating a using b, x and y
a 5 0.15407 x 33.5 = -0.1613
The Equation of least square line is
y -0.1613 0.154x
help_outline

Image Transcriptionclose

a y bx Σx, Σν: 16 n i1XiVi b = 2. - (2*) 16 i=1 ΣΕ1 Li 1 Putting values, to calculate b first 6 x 1163 201 x 30 b = 0.15407 6 x 7759 2012 Σν 30 5 6 n Σχ 201 33.5 6 n Calculating a using b, x and y a 5 0.15407 x 33.5 = -0.1613 The Equation of least square line is y -0.1613 0.154x

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