5 This is a cross-sectional data set on 526 working individuals for the year 197

Question

5

This is a cross-sectional data set on 526 working individuals for the year 1976. Estimate:

where Wage is in $ per hour, education is years of schooling, and experience is years of working experience.

a) Interpret the coefficient attached to Education.

b) Predict the hourly wage of an individual with 15 years of education and 10 years of experience (be careful to make the correct adjustment!).

c) Is Experience2 statistically significant at the 5% level?

d) Are Experience and Experience2 jointly significant at the 5% level?

e) Given the original model, what is the value of Experience that maximizes the ln(Wage)?

Wage Education Experience 3.1 11 2 3.2 12 22 3 11 2 6 8 44 5.3 12 7 8.8 16 9 11.3 18 15 5 12 5 3.6 12 26 18.2 17 22 6.3 16 8 8.1 13 3 8.8 12 15 5.5 12 18 22.2 12 31 17.3 16 14 7.5 12 10 10.6 13 16 3.6 12 13 4.5 12 36 6.9 12 11 8.5 12 29 6.3 16 9 0.5 12 3 6 11 37 9.6 16 3 7.8 16 11 12.5 16 31 12.5 15 30 3.3 8 9 13 14 23 4.5 14 2 9.7 13 16 5 12 7 4.7 12 3 4.3 16 22 6.2 12 15 3.5 4 39 3 14 3 6.3 12 11 7.8 12 3 10 12 20 4.5 14 16 4 11 45 6.4 13 11 13.7 15 20 1.7 10 1 2.9 12 36 3.7 14 9 2.9 12 15 1.6 12 18 8.6 16 3 5 12 15 6 12 7 2.5 12 2 3.3 15 3 3.4 16 1 10 8 13 21.6 18 8 4.4 16 7 11.7 13 40 12.4 14 42 6.3 10 36 3.7 10 13 7.8 14 9 20 14 26 6.3 16 7 10 12 25 5.7 16 10 2 12 3 5.7 16 3 13.1 17 17 4.9 12 17 2.9 12 20 3.8 12 7 11.9 13 24 4 12 28 3.1 12 2 8.5 12 19 7.1 18 13 4.5 9 22 4.7 16 3 2.9 10 4 6.7 12 7 3.5 12 6 3.3 12 13 3.3 12 14 8 12 14 9.9 8 40 7.5 12 11 5.9 12 14 11.8 14 40 3 12 1 4.8 12 2 6.5 12 4 4 9 19 3.5 13 1 13.2 12 34 4.3 14 5 3.5 12 3 5.1 15 6 3.8 12 14 4.5 12 35 7.6 12 8 15 14 7 6.9 15 11 13.3 12 14 6.7 12 35 2.5 12 46 9.8 17 7 3.4 11 45 25 18 29 5.4 12 6 6.1 14 15 4.2 14 33 3.8 10 15 3.5 14 5 3.6 12 7 3.8 15 6 3 8 33 5 16 2 4.6 14 4 3 15 1 3.2 12 29 3.9 18 17 6.4 16 17 5.5 10 36 1.5 8 31 2.9 10 23 5 11 13 8.9 18 3 5 15 15 3.5 12 48 2.9 11 6 4.5 12 12 2.3 12 5 5 14 19 10 16 9 3.8 2 39 10 14 28 11 16 23 7.9 12 2 4.7 12 15 5.8 13 5 3.8 12 18 3.2 15 2 2 10 3 4.5 12 31 11.6 16 20 2.1 13 34 2.4 9 5 3.8 12 11 5.5 13 31 6.5 12 8 3.1 12 2 10 14 18 6.6 16 3 10 16 3 2.3 9 4 6.9 18 4 2.8 10 1 3.1 10 1 8 13 28 4.5 12 47 8.7 18 13 2 13 2 4.8 12 48 6.3 13 6 6 13 8 15.4 13 25 14.6 18 13 12.5 12 8 5.3 12 19 2.2 13 1 7.1 12 43 6.2 12 19 9 12 11 10 14 43 5.8 10 44 4 12 22 8.8 16 3 6.5 16 3 7.6 12 41 5 14 5 5 12 14 21.9 12 24 8.6 12 28 3.3 12 25 4.4 12 3 4.6 12 11 3.5 12 7 6.3 16 9 3.9 16 5 6.2 14 9 2.9 11 1 6.3 16 2 6.3 12 13 9.1 12 10 10 17 5 11.1 12 30 6.9 12 31 8.8 16 1 10 8 9 3.1 12 10 3 12 38 5.8 12 19 4.1 16 5 8 12 26 6.2 12 35 2.7 9 2 2.8 13 1 3 16 19 3 14 3 7.4 8 36 7.5 14 29 3.5 13 1 8.1 12 38 3.8 18 1 3.3 9 29 5.8 8 36 3.5 8 4 3.3 12 45 4 14 22 3.5 12 20 6.3 16 5 3 8 15 5.7 13 10 3 9 3 22.9 16 16 9 12 38 8.3 15 33 3 11 2 5.8 14 6 6.8 12 19 10 12 29 3 12 2 3.5 18 3 3.3 12 4 4 12 10 2.9 12 4 3.1 12 14 3.2 12 15 4.8 12 19 3 14 17 18.2 16 29 3.5 12 2 4.1 14 5 2 11 38 4.3 12 3 3 10 47 6.5 12 7 5.2 6 47 4.5 13 23 3.9 12 12 3.5 10 11 10.9 12 25 4.1 14 6 3 13 3 5.9 12 14 18 18 13 4 12 9 3 12 1 3.6 12 6 3 12 11 8.8 12 47 2.9 8 49 6.3 13 37 3.5 13 2 4.6 14 7 6 12 22 2.9 10 8 5.6 16 1 4 12 43 6 16 2 4.5 12 2 2.9 14 1 4.3 18 1 18.9 17 26 4.3 13 1 4.6 14 37 6.3 15 12 3 14 41 8.8 12 24 8.5 8 38 3.8 12 18 3.2 12 26 5 8 45 6.5 12 27 2 9 2 4.8 12 41 5.8 16 11 3.2 12 5 4.7 16 3 4.1 12 3 2.9 12 4 6 13 21 3.6 10 34 4 6 49 7 12 6 3 12 26 6.1 16 9 8.6 12 23 3 8 33 3.8 12 5 2.9 6 49 3 4 48 6.3 11 35 3.5 11 23 3 7 26 3.2 12 16 8 18 23 3.3 12 36 5.3 16 4 6.3 12 10 3.5 14 18 3 12 3 3 10 7 4.7 10 7 3.7 9 33 4 10 34 4 12 8 2.9 12 17 3.1 12 2 5.1 10 5 14 16 41 18.2 16 35 6.3 16 11 5.3 12 4 4.8 12 12 3.4 7 35 3 8 33 8.4 16 8 5.7 16 2 12 18 8 3.5 13 29 4.2 10 14 7 16 26 6 14 11 12.2 16 10 4.5 12 13 3 9 23 2.9 11 1 15 11 35 4 12 5 5.3 11 13 4 12 22 3.3 12 21 5.1 12 19 3.6 12 13 5 14 15 4.6 14 3 12.5 18 6 3.5 12 6 4.6 12 16 10 12 31 2.9 11 1 4.5 12 5 6.5 17 3 7.5 16 11 3.5 13 6 4.2 13 11 3.5 12 7 4.5 14 5 3.4 14 5 2.9 11 2 5.3 10 44 4.1 8 44 3.8 14 13 3.4 12 26 3 10 2 6.3 17 10 2.5 9 2 4.5 12 35 3.1 12 6 6.4 14 8 4.7 16 1 6.8 12 14 8.5 10 14 4.2 0 22 3.8 14 8 11.1 15 1 3.3 16 15 9.1 12 14 4.5 11 37 3 11 1 8.8 12 4 4.1 13 29 2.9 12 45 3.4 13 22 6.1 16 42 3 15 9 4.2 16 8 5.6 15 31 10 12 24 12.5 18 16 3.8 6 6 3.1 6 14 4.3 12 47 10.9 12 34 7.5 16 6 4.1 9 7 4.7 12 27 5 11 24 2.9 10 18 8 12 12 8.4 8 27 2.9 9 49 6.3 17 4 6.3 16 24 5.1 11 3 4 10 2 4.4 8 29 6.9 13 34 5.4 14 10 3 13 5 2.9 11 2 6.3 7 39 4.3 16 5 3.3 12 14 7.3 13 8 6.4 14 10 5.6 16 2 8.8 14 9 3.2 11 1 3 8 45 3 14 33 12.5 17 21 2.9 10 2 3.4 12 9 6.5 12 33 10.4 18 16 4.5 14 10 10 18 9 3.8 12 8 8.8 16 9 9.4 14 23 6.3 12 23 4 9 22 2.9 12 37 20 12 22 11.3 17 28 3.5 12 14 6 15 19 14.4 17 10 6.4 16 25 3.6 12 21 3 15 32 4.5 16 21 6.6 12 36 9.3 15 2 3 12 11 3.3 12 40 1.5 12 11 5.9 12 9 8 16 23 2.9 11 1 3.3 14 30 6.5 14 41 4 13 6 6 14 11 4.1 12 43 3.8 12 39 3.1 8 50 3.5 12 26 2.9 3 51 4.5 11 3 3.4 15 3 6 11 15 8 12 17 3 4 36 5 9 31 5.5 12 9 2.7 12 42 3 11 3 4.5 12 37 17.5 16 23 8.2 13 21 9.1 15 11 11.8 16 35 3.3 12 42 4.5 12 3 4.5 12 13 3.7 9 14 6.5 10 14 2.9 12 39 5.6 11 11 2.2 8 28 5 6 18 8.3 16 6 2.9 12 26 6.3 12 21 4.6 16 34 3.3 12 17 2.3 10 2 3.3 13 5 3.2 13 1 12.5 14 40 5.2 16 39 3.1 10 1 7.3 12 14 2.9 12 2 1.8 11 2 2.9 0 42 2.9 5 34 17.7 16 10 6.3 16 4 2.6 9 4 6.6 15 21 3.5 12 31 6.5 12 20 3 12 36 4.4 13 7 10 12 15 5 7 25 9 17 7 1.4 12 17 3.1 12 3 9.3 14 12 7.5 12 18 4.8 13 47 5.7 12 2 15 16 14 2.3 10 2 4.7 15 13 11.6 16 5 3.5 14

5

In (Wagei) = 0 + ,Education, + 2Experience, + 3Experience? +

Explanation / Answer

Regression Analysis: Log(Wage) versus Education, Experience, Exp^2

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 3 44.484 14.8279 74.52 0.000
Education 1 29.104 29.1044 146.27 0.000
Experience 1 12.339 12.3393 62.01 0.000
Exp^2 1 7.517 7.5172 37.78 0.000
Error 522 103.865 0.1990
Lack-of-Fit 238 57.573 0.2419 1.48 0.001
Pure Error 284 46.293 0.1630
Total 525 148.349

Model Summary

S R-sq R-sq(adj) R-sq(pred)
0.446067 29.99% 29.58% 28.93%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 0.130 0.106 1.23 0.219
Education 0.09035 0.00747 12.09 0.000 1.13
Experience 0.04094 0.00520 7.87 0.000 13.13
Exp^2 -0.000712 0.000116 -6.15 0.000 13.43

Regression Equation

Log(Wage) = 0.130 + 0.09035 Education + 0.04094 Experience - 0.000712 Exp^2

b)Prediction for Log(Wage)

Regression Equation

Log(Wage) = 0.130 + 0.09035 Education + 0.04094 Experience - 0.000712 Exp^2

Variable Setting
Education 15
Experience 10
Exp^2 100

Fit SE Fit 95% CI 95% PI
1.82386 0.0269643 (1.77089, 1.87683) (0.945955, 2.70177)

C) Experience ^2 is statistically significant at 0.05 level

d) Both are significant at 0.05 level to the output.

e) maximum ln(Wage)= 3.21888, Education= 18, Exp= 29 and Exp^2= 841

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