Question

An economist was interested in modeling the relation among annual income, level of education, and work experience. The following data was obtained from a random sample of 12 individuals. Level of education is the number of years of education beyond eighth grade, so 1 represents completing 1 year of high school, 8 means completing 4 years of college, and so on. Work experience is the number of years employed in the current profession. Annual income is measured in thousands of dollars.
Work Experience Level of Education Annual Income ($ Thousands)
21 6 34.7
14 3 17.9
4 8 22.7
16 8 63.1
12 4 33.0
20 4 41.4
25 1 20.7
8 3 14.6
24 12 97.3
28 9 72.1
4 11 49.1
15 4 52.0

A) Construct a correlation matrix between work experience, level of education, and annual income. Is there any reason to be concerened with multicollinearity based on the correlation matrix?

Answer 1

Answer:

Check the explanation

Step-by-step explanation:

A) We use Minitab to solve the question.

The correlation matrix is,

Correlation: Level of Education, Work Experience, Annual Income ($ ,000s)

Work Experience Level of Education

Level of Education -0.042 0.463

Annual Income ($ 0.463 0.756

From correlation matrix there is no any reason to concern multicoinearity.

B)

The Regression Analysis: Annual Income ($ Thousands) vs Work Experience and Level of Education

Analysis of Variance

Source D F Adj SS Adj MS F-Value P-Value

Regression 2 5577 2788.4 19.96 0.000

Work Experience 1 1675 1674.7 11.99 0.007

Level of Education 1 4114 4114.1 29.44 0.000

Error 9 1257 139.7

Total 11 6834

Model Summary

S R-sq R-sq(adj) R-sq(pred)

11.8204 81.60% 77.51% 69.81%

Coefficients

Term Coef SE Coef T-Value P-Value VIF

Constant -15.2 10.2 -1.49 0.171

Work Experience 1.545 0.446 3.46 0.007 1.00

Level of Education 5.57 1.03 5.43 0.000 1.00

E)

The value of R-sq is 81.60% & R-sq (adj) is 77.51% indicates that adequacy of the fitted model is good.

G & H )

Coefficients

Term Coef SE Coef T-Value P-Value

Constant -15.2 10.2 -1.49 0.171 > 0.05 (significant)

Work Experience 1.545 0.446 3.46 0.007 > 0.05 (significant) ______Reject H0 B1 = 0

Level of Education 5.57 1.03 5.43 0.000 < 0.05 (Not Significant) ______do not Reject H0 B2 = 0

H)

Regression Equation

Annual Income ($ Thousands) = -15.2 + 1.545 Work Experience + 5.57 Level of Education

= -15.2 + 1.545 * 12 + 5.57 * 4

= 25.62

I & J)

Regression Equation

Annual Income ($ Thousands) = -15.2 + 1.545 Work Experience + 5.57 Level of Education

Variable Setting

Work Experience 12

Level of Education 4

Predicted Income is 25.5649 thousands:

Kindly check the attached image below.

Fit SE Fit 95% CI 95% PI

25.5649 4.42545 (15.5538, 35.5759) (-2.98733, 54.1170)