Question

t An economist is studying the job market in Denver area neighborhoods. Let x entry-level jobs in the same nelghborhood. A sample of six Deniver neghborhoods gave the folowing iformacion (ents in hundreds of yobs) represent the total number of jobs in a given neighborhood, and let y represent the number Complete parts (a) therough te), given x-201, y-27,-7759,-161, By-1082, and r0.882 () Draw a scer dagram dsplaying the data 1. Select an n Object Properties to place and move ebijets Object Properties Caps Locih nspiron 13 7000

Answer 1

a)Scatter plot is given as below

Scatter plot 10 ◆Y 10 30 40 0 20 50 60

b)

Below table shows the calculations

	X	Y	X*Y	X^2	Y^2
	15	1	15	225	9
	32	3	96	1024	36
	51	6	306	2601	25
	28	5	140	784	81
	50	9	450	2500	9
	25	3	75	625	729
Sum	201	27	1082	7759	889

Y-27 У-

$\sum X=201$

X × yー1082

X2-7759

-2-889

Value of Correlation Coefficient is given by below formula

By substituting the above values we find the value of r =0.88

Which lies between 0.5 and 1

Which indicates that there is strong positive linear relationship

c)

15 + 32 +51 + 28 + 50+25 6 201 6 33.5

1+3+6+5+9+327 6 4.5 6

The regression equation is

Y=a+bX

From Excel with below mentioned steps We would find the regression summary

Select Data>Data Analysis>Regression>Select input and Output Range>Ok

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.881925657
R Square	0.777792864
Adjusted R Square	0.72224108
Standard Error	1.481315451
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	30.72281814	30.72281814	14.00122209	0.020089256
Residual	4	8.777181863	2.194295466
Total	5	39.5
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-1.29839103	1.663439351	-0.780546058	0.478679077	-5.916839074	3.320057016	-5.916839074	3.320057016
X	0.173086299	0.04625724	3.741820691	0.020089256	0.044655611	0.301516988	0.044655611	0.301516988

So regression Equation is given as

Y=-1.29+0.17X

d)

Graph of least square line is given as below:

Option A is correct whose graph is shown as below

8 4 2 0 2 4 6 2 6

e)

From the above regression summary output is

Coefficient of determination R square is given as 0.77

It means 77% variation is explained variation

& 23% variation is unexplained

f)

Predicted value of Y when X=43

Using the fitted regression equation

Y=-1.29+0.17X=-1.29+0.17(43)=6.02

Predicted value will be 6.02