An economist is studying the job market in Denver area neighborhoods. Let x repr

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 34 52 28 50 25

y 1 4 5 5 9 3

Complete parts (a) through (e), given x = 202, y = 27, x2 = 7938, y2 = 157, xy = 1074, and r 0.821.

(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-bar= ______

y-bar= ______

y-hat= + __________ x

(e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explainedby 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 = 34 hundred jobs, how many are predicted to be entry level jobs? (Round your answer to two decimal places.)
__________ hundred jobs

x = y = x2 = y2 = xy = r =

Explanation / Answer

b)

C)

The regression equation is

y=a+bx

From Excel

The fitted Regression model is

y hat= -0.38 +0.145 (X)

e)

r2=0.674

f) when x=34

then y hat= -0.38 +0.145 (X)

y hat=4.55

The fitted regression is

y hat=12.75 +4.65 (

X Y X^2 Y^2 XY 13 1 169 1 13 34 4 1156 16 136 52 5 2704 25 260 28 5 784 25 140 50 9 2500 81 450 25 3 625 9 75 Sum= 202 27 7938 157 1074 Means= 33.66667 4.5

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