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	14	35	50	28	50	25
y	1	4	5	5	9	3

1) A. given Σx = 202, Σy = 27, Σx² = 7830, Σy² = 157, Σxy = 1069, and r ≈ 0.837.

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 =

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

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 = 32 hundred jobs, how many are predicted to be entry level jobs? (Round your answer to two decimal places.)
hundred jobs

Answer 1

Computational Table:

	X	Y	X^2	Y^2	XY
	14	1	196	1	14
	35	4	1225	16	140
	50	5	2500	25	250
	28	5	784	25	140
	50	9	2500	81	450
	25	3	625	9	75
Total	202	27	7830	157	1069

Correlation coefficient = r :

r = 0.837

Σx = 202.

Σy = 27

Σx2 = 7830

Σy2 = 157

Σxy = 1069

r = 0.837

Calculation:

For Slope:

b = 0.155

For Intercept:

a = 4.50 - 0.155*33.67

a = -0.733

Therefore, the least square regression line would be,

= -0.733 + 0.155 (X)

Coefficient of Determination (R2):

R2 = 0.8372 = 0.701

explained = 70.1%

Unexplained = 29.9%

f)

The least square regression line would be,

= -0.733 + 0.155 (X)

For X = 32

= -0.733 + 0.155*32

= 1.60  

1.60 hundred jobs