College

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 concerned with multicollinearity based on the correlation matrix?

Answer :

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)

Other Questions