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	16	32	52	28	50	25
y	1	3	5	5	9	3

Complete parts (b) through (e), given Σx = 203, Σy = 26, Σx² = 7893, Σy² = 150, Σxy = 1037, and r ≈ 0.804.

(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 = 37 hundred jobs, how many are predicted to be entry level jobs? (Round your answer to two decimal places.)
______ hundred jobs

Answer 1

	n=	6.0000
	X̅=ΣX/n	33.8333
	Y̅=ΣY/n	4.3333
	sx=(√(Σx2-(Σx)2/n)/(n-1))=	14.3167
	sy=(√(Σy2-(Σy)2/n)/(n-1))=	2.7325
	Cov=sxy=(ΣXY-(ΣXΣY)/n)/(n-1)=	31.4667
	r=Cov/(Sx*Sy)=	0.804
	slope= β̂1 =r*Sy/Sx=	0.1535
	intercept= β̂0 ='y̅-β1x̅=	-0.8608

from above:

b)

ΣX =	203.000
ΣY=	26.000
ΣX2 =	7893.000
ΣY2 =	150.000
ΣXY =	1037.000
r =	0.804

c)

X̅=ΣX/n =	33.83
Y̅=ΣY/n =	4.33
ŷ =	-0.861+0.154x

d)

e)

coeff of determination r2 =		0.647
explained =		64.7%
unexplained=		35.3%

f)

predicted val=-0.8608+37*0.1535=

4.82