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 13 33 50 28 50 25 y 1 2 6 5 9 3 Complete parts (a) through (e), given ?x = 199, ?y = 26, ?x2 = 7667, ?y2 = 156, ?xy = 1044, and r ? 0.845. (a) Draw a scatter diagram displaying the data. (b) Verify the given sums ?x, ?y, ?x2, ?y2, ?xy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) ?x = ?y = ?x2 = ?y2 = ?xy = 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 = 40 hundred jobs, how many are predicted to be entry level jobs? (Round your answer to two decimal places.) hundred jobs

Answer 1

Solutionb:

sums verified:

	X	Y	X^2	Y^2	XY
	13	1	169	1	13
	33	2	1089	4	66
	50	6	2500	36	300
	28	5	784	25	140
	50	9	2500	81	450
	25	3	625	9	75
TOTALS	199	26	7667	156	1044

In excel go to

insert >scatterchart

You get below plot

In excel go to

data >data analysis>Regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.844921
R Square	0.713891
Adjusted R Square	0.642364
Standard Error	1.760544
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	30.93527	30.93527	9.980679	0.03421
Residual	4	12.39806	3.099516
Total	5	43.33333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-1.31448	1.926796	-0.68221	0.532563	-6.66413	4.035161
X	0.170286	0.053901	3.159221	0.03421	0.020632	0.31994

regressin equation is

y=-1.314+0.170x

Solutione:

R sq=0.713891

=0.713891*100

=71.389%

71.389% is explained

100-71.389=28.611% unexplained.

Solutionf:

For X=40 substitue in Reg eq

y=-1.314+0.170*40

y=5.49

e predicted to be entry level jobs=5.49