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	17	30	48	28	50	25
y	3	4	7	5	9	3

Complete parts (a) through (e), given Σx = 198, Σy = 31, Σx² = 7402, Σy² = 189, Σxy = 1172, and r ≈ 0.942.

(a) Draw a scatter diagram displaying the data.

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(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 = 41 hundred jobs, how many are predicted to be entry level jobs? (Round your answer to two decimal places.)
hundred jobs

Answer 1

a)

b)

ΣX =	198.000
ΣY=	31.000
ΣX2 =	7402.000
ΣY2 =	189.000
ΣXY =	1172.000
r =	0.942

c)

X̅=ΣX/n =	33.00
Y̅=ΣY/n =	5.17
ŷ =	-0.498+0.172x

e)

coefficient of determination r2 =		0.887
explained =			88.7%
unexplained=			11.3%

f)

predicted value =-0.498+0.172*41=

6.55