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	18	31	51	28	50	25
y	1	4	7	5	9	3

Complete parts (a) through (e), given Σx = 203, Σy = 29, Σx² = 7795, Σy² = 181, Σxy = 1164, and r ≈ 0.940.

(a) Draw a scatter diagram displaying the data.

(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=Σx =
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.)

(f) For a neighborhood with x = 30 hundred jobs, how many are predicted to be entry-level jobs? (Round your answer to two decimal places.)
hundred jobs

Answer 1

b)

Σx = 203,

Σy = 29,

Σx² = 7795,

Σy² = 181,

Σxy = 1164,

r ≈ 0.940

c)

xbar =33.83

ybar=4.83

yhat=-1.841+0.197x

e)

coefficient of determination r² =0.883

explained % =88.3%

unexplained % =11.7%

f)

predicted value =-1.841+0.197*30=4.07 (try 4.08 if this comes wrong)