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

Complete parts (a) through (e), given Σx = 202, Σy = 27, Σx2 = 7830, Σy2 = 157, Σxy = 1069, and r ≈ 0.837.

(a) I ALREADY COMPLETED THIS QUESTION

(b) I ALREADY COMPLETED THIS QUESTION

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

Answer 1

C)

For slope:

b = 0.16

For Intercept:

a = 4.5 - (0.16*33.67)

a = -0.73

Therefore, the least square regression line would be,

d)

e) Find Coefficient Determination (R²)

R² = {Correlation coefficient (r)}² = 0.837² = 0.701

70.1% of variation can be explained

and remaining, 29.9% of variation be Unexplained.

f)

For a neighbourhood with x = 32 hundred jobs