Using the WAGE/EDUC data in the DATA worksheet estimate the log-linear model, E[

Question

Using the WAGE/EDUC data in the DATA worksheet estimate the log-linear model, E[ln(WAGE)] = + EDUC. The "generalized" R² for the model is?

WAGE EDUC 18.7 16 11.5 12 15.04 16 25.95 14 24.03 12 20 12 53.84 16 25 12 28.85 16 16.83 13 14.8 12 43.25 16 19.23 12 14 14 8 12 57.7 21 20 12 20.83 18 22 11 68.75 14 10.5 12 9.88 13 10.96 12 8.25 13 14.86 18 8.75 12 15.3 12 12.7 12 10.75 13 17.33 12 7.5 10 18.5 12 9 13 51.29 21 20.53 14 12.68 18 7.25 12 18.28 14 21.63 16 19.23 14 25 12 16.83 16 10.53 12 16.35 13 5.2 13 50 13 10 13 9 12 13 14 18.25 12 36.05 16 11.3 12 11 10 7.5 12 7.5 16 25.63 12 25.95 18 19.23 16 25 13 28 14 9 3 29.75 12 8.75 3 15.55 12 25.63 14 17.19 18 10.5 12 12.7 14 9.46 12 28.85 18 47.13 16 9 14 72.13 12 30.77 21 28.84 16 26.93 14 8 12 8 13 18.75 13 13 13 34.62 21 39.9 13 10.25 16 15.37 12 19.23 12 13.45 12 27.5 13 10 14 13.03 12 7.88 12 8 6 16.83 16 13.8 12 10.3 13 11.5 14 12 16 35.89 18 28.85 16 16.95 12 17 14 8 14 40.38 16 20 13 19.23 13 10 16 35.71 16 39.06 14 9 18 13.5 12 31.25 18 19.23 12 29.91 16 13.5 12 15 16 32.68 13 29.08 16 27.83 14 14.25 12 38.47 16 18.28 12 20 16 9 14 12 12 12 16 25.63 18 22.05 13 10.5 16 6.76 9 6.5 10 9.32 13 10.58 12 24.03 16 18 12 18.03 14 39.23 18 18.52 12 24.05 16 28.85 13 9.57 10 14.95 13 15.65 13 25 18 27.88 21 15.4 13 19.23 14 38 16 15.38 12 28.85 13 15.88 13 25 16 11.35 14 15.38 12 30.76 16 18.75 12 72.13 16 13.75 12 24.05 13 17.5 12 43.25 18 9.93 12 24.63 16 36.3 13 30.9 16 11 14 12.5 12 28.85 13 10 12 25.35 16 12.31 13 21.27 12 17.49 12 23 13 36.05 18 9 12 27.3 13 21.63 16 17 13 14.29 16 35.1 18 16 12 7 12 21.63 12 9.25 14 15.43 12 21.25 16 34.63 12 10 16 15.38 16 45.23 14 12 16 10 12 14 13 31.25 12 50.95 18 37.5 21 15.88 13 23.08 12 8.52 0 10 14 18 14 31.73 13 20 16 28 18 7.25 9 14.4 16 21.63 12 24.05 13 21 13 24.29 16 6 14 12.5 12 19.23 12 15.53 12 7.25 11 35.49 18 19.24 18 22.7 18 30.7 18 10 13 72.13 16 72.13 16 19.23 14 9.9 13 15 8 6.5 13 28.72 12 34.63 18 12.03 13 9 14 30 16 3.75 16 16.83 14 12.08 12 43.8 21 8.25 13 19.55 14 21.54 16 14.5 12 10.5 8 11.3 13 35 12 19.55 14 10.94 12 13.33 12 18 12 9.5 12 18 12 15 18 13 12 19.2 14 11.5 12 36.52 16 10 12 20.04 13 24.03 16 31.25 14 13.04 13 16 12 31.25 12 16.88 16 29.8 13 7.6 12 11 13 16.28 16 17.57 13 24.33 16 16.24 16 22 16 25 12 20 13 43 12 40.38 16 11.5 13 19.23 13 7.5 13 19.23 16 21.5 12 26 14 16.08 18 14 16 23.06 16 13.25 12 61.11 18 11.25 13 16.83 16 8 13 8.63 12 18.75 14 30.33 18 40.46 13 27.63 16 11 16 7.5 13 17.88 16 8 13 18.3 12 28.83 13 13 12 25.32 12 18.9 12 17.86 12 9.26 12 18.49 12 14.43 12 24.05 18 6.87 16 19.24 18 24.05 18 20.09 16 26 12 21.15 16 27.4 13 38.45 16 12.86 12 10.3 12 11 16 15.13 12 24.05 14 13 12 20.2 16 7.5 11 8 13 7.25 8 11.5 13 24.05 13 24.05 12 13.73 13 7.93 13 8.75 16 13.2 10 15 12 15.39 12 8 12 35.25 16 14.68 18 12.4 12 12.5 13 10 12 21.67 18 20 12 13.08 14 7 12 19.23 16 15 14 6.5 12 8.5 12 6.35 12 19.24 14 20.63 13 24.05 3 48.55 18 13.16 16 12.75 12 19.57 16 8.53 13 10 13 24.33 12 11 14 33.65 18 14.91 16 14.16 12 10.78 13 21.36 16 38.23 12 36.71 13 6.25 18 27.1 16 10 12 8 16 7.5 12 10.38 13 13.73 16 54.05 16 17.3 12 20.3 14 7.14 12 25 16 31.15 14 9.5 12 8.1 12 8.5 12 25.96 14 13.75 16 12.5 14 9 12 57.69 16 72.13 14 36.05 16 19.79 12 50 18 7.49 12 16 12 40.38 21 33.65 16 38.45 18 52.88 16 13 12 24.05 12 8.75 16 40.38 18 8.8 12 15.56 16 10 12 9.34 11 10.5 12 18 12 6.93 12 17.5 6 24.05 16 12.31 12 32.7 12 9.5 12 17.5 16 25 16 14.43 13 9.33 13 17.48 12 12.5 12 8 12 17.3 12 15.38 12 6.5 8 44.43 16 15.85 14 14.4 12 7.29 14 19.7 18 21 14 11 12 16.57 14 48.55 16 12 12 40.15 16 22.4 12 11.5 13 28.85 12 24.23 14 24.05 16 7.5 9 11.25 13 19.23 16 12.98 13 16.56 13 23 12 12 12 53.57 18 8.85 11 47.8 16 20 14 1.97 18 10.51 12 9 13 9.73 14 38.45 16 28 16 27.23 12 13.03 12 30 16 10.1 14 16.25 12 15.25 12 35 13 57.68 21 50 16 9.63 12 10 14 15.23 12 10.5 12 10 16 20.1 12 8 12 17 13 35.17 18 9 13 12.9 16 12.75 9 24.05 18 10.19 12 38.45 14 14.25 12 12.03 6 19.23 13 8.75 14 29.1 13 33.65 16 16 12 13.88 3 25 12 15 13 25.18 13 17.5 12 36.8 18 32.68 18 28.83 16 25.25 13 16 10 18 12 14.5 12 41.35 18 16.25 14 9 13 17.71 13 15.45 14 23.08 12 8 13 13.75 12 8.76 9 8.78 13 7.75 6 28.85 16 20.2 16 9.23 12 14 16 25 12 21.48 12 12.97 13 27 12 37.5 12 21.15 14 2.88 13 9.75 11 16 12 13 12 48.08 21 7.7 12 22.6 18 5.73 6 14.4 12 33.5 12 18.82 11 17.5 12 11 16 9.35 16 16.25 6 9.5 13 76.39 14 36.67 18 9 18 51.52 13 15 21 38.75 18 15.38 16 43.28 21 17.3 16 33.65 16 2.5 12 16.25 12 14.6 12 12.5 16 36.05 21 19.23 12 9.24 12 9.15 13 36.05 16 16.25 12 14.55 12 29.4 21 50.03 13 28 16 28.83 16 72.13 16 13 16 6.14 11 36.33 16 18.06 12 22.64 14 15 14 42.11 16 13.8 13 55 16 10.4 13 24.03 16 20.63 16 12.5 16 24.95 13 23.49 16 28 14 9.5 13 34.63 14 48.55 16 8.06 13 17.36 13 28.44 14 35.75 14 13.95 14 9 12 21 13 20 12 8.33 13 65.98 21 13 12 21.33 12 15 16 8.1 11 15 9 15 12 18.75 18 9.78 12 9.83 12 10 12 12.5 12 30.44 16 12.5 13 13.45 12 29.8 13 26.78 16 10 18 21.52 18 12.87 12 22.5 16 15 12 24.79 12 6.66 12 10.73 14 10.5 12 13.16 10 9.75 12 17 12 36.05 14 41.54 16 34.18 12 50 18 6.73 12 6.38 18 20.6 16 6.75 12 10 13 26.78 12 72.13 18 21.63 16 44.23 18 17.35 13 25.73 14 50 16 20 14 8 12 34.63 14 9.5 13 7.7 3 9 16 16 13 8.75 12 11 12 13.82 16 13.1 12 19.23 14 18.45 12 14.43 13 21.93 16 16.1 14 14.5 13 15.71 16 28.18 12 28.85 14 57.7 16 28.85 18 23.08 13 25.25 18 15 12 23.08 16 21.88 13 8.26 12 12.03 16 8.5 12 40 16 30 6 28 21 9.5 12 23.07 16 22.3 16 7.52 12 38.45 18 18.75 8 2.52 12 26.14 12 36.06 13 12 16 15.38 14 16.23 12 31.25 16 20 14 10.38 13 9.48 12 25 13 10.49 14 11.5 12 8 12 14.5 16 38.45 18 11.5 11 45.65 8 14 12 5.33 12 12.9 16 23.63 16 30.3 16 20.2 16 31.25 18 26.44 13 23 12 32.68 14 18.25 13 20.2 12 22.6 12 7.45 10 13 12 8 12 26.1 12 46.16 16 8 12 16 12 8.76 16 33.65 12 11.78 13 47.62 18 24.45 12 34.18 16 31.73 16 18.45 12 34.62 13 21.36 12 38.46 18 2.3 16 22.65 13 4.33 8 31.25 18 8.5 14 22.76 13 19.55 12 17.96 14 24.04 12 44.24 12 31.88 14 28.83 21 39.9 14 61.82 18 25.38 16 12 16 8.65 16 38.45 16 38.45 10 7.2 12 7.5 13 25 14 18.48 16 61.54 18 15.8 12 39.43 12 10 12 6.25 21 28.85 18 15.33 12 23.3 18 9 12 21.8 13 15.33 12 10 12 20.17 16 25.64 16 10.5 13 10.38 13 16.83 16 15.75 12 19.24 14 8.65 12 10.85 16 18.7 13 16.22 11 9 9 12 12 6.77 12 20.13 14 15 13 10 12 12 12 17.96 16 37.6 16 14.43 13 42 16 41.52 13 23.08 16 24.53 16 9.52 13 12 16 13.8 12 42 13 10.55 12 10 13 12.75 14 8.75 12 28.85 16 25 16 25 18 25 16 9 12 72.13 18 21.03 16 35.23 16 9.4 12 12.5 13 37.5 14 6.5 12 52.5 13 7.5 14 31.25 16 25 18 10.48 12 17.75 12 13 13 5.97 12 25 21 18.5 13 11.55 11 44.87 16 7.4 8 11.85 12 24.17 16 7.2 14 18.18 13 14 12 36.05 13 13.61 12 34.63 16 17.3 16 14 14 29.9 18 15 13 16.14 18 38 16 7.98 12 24.03 18 23.51 21 22.43 21 15.75 13 11.5 13 21.63 18 45.45 18 35.63 12 19.05 9 30.63 13 16.35 14 12.4 12 31.25 12 14.1 14 24 14 27.49 16 7.9 12 11 12 16.83 12 57.68 16 11 16 6.4 12 16.83 14 19.58 11 28.52 12 12 12 21.15 13 14.9 12 14.26 12 8.15 11 32.3 16 7 12 22.5 12 30 13 24.14 16 72.13 18 11.8 14 60.1 18 19.23 12 12.82 16 15 16 21.25 14 11.51 6 28.83 12 25.64 21 12.26 16 10 12 8 12 25.48 16 52.88 21 19.22 16 19.23 18 15 12 19.23 16 23.58 13 4.58 12 9 12 15 12 25 13 29.8 18 64.11 18 19.23 14 27.4 12 21.63 12 10 12 11.55 13 38.45 16 17 12 64.11 16 28.1 14 21.25 8 10.58 12 16.67 10 31.75 16 25.75 13 17.42 13 21.63 16 7.97 13 48.08 18 21.25 16 10 14 19.63 12 16 12 19.23 16 28.85 12 8.5 12 60 14 9.63 12 9 13 37.18 12 33.65 13 16.25 12 14.43 16 10 12 19.23 16 19.23 18 7 11 24.03 21 7.57 13 12.5 12 11.4 13 13 16 25 12 22.13 12 13.5 13 8 12 11.25 12 14.43 12 9.8 18 17.3 12 8 12 35.76 16 10 12 19.23 16 20 14 10.25 16 17.63 12 14.53 13 5.9 14 18.46 12 39.33 12 7.5 11 16 18 14.5 13 62.03 16 16.35 12 24.44 12 17 13 14.96 16 67.3 12 21 13 20.4 16 16 10 12.82 14 20 18 12 12 35.1 16 12.5 13 31.73 16 12.38 8 12.5 12 21 14 21.38 13 12.5 12 57.7 12 29.76 13 18 12 7.25 13 9 14 27.7 21 28 3 12 16 9.7 13 7 12 18.24 21 25.95 18 16.04 16 14 12 40.08 18 8 12 16.93 16 11.5 12 21.15 13 7.2 16 23.1 12 16.83 16 28.85 13 11.25 14 7.5 8 8.5 13

Explanation / Answer

First i took Logarithm of the wages and then did a linear regression in excel. Following is the result

so R2 = 0.1782

as given in the table.

SUMMARY OUTPUT Regression Statistics Multiple R 0.422143 R Square 0.178205 Adjusted R Square 0.177381 Standard Error 0.526611 Observations 1000 ANOVA df SS MS F Significance F Regression 1 60.01584 60.01584 216.4141 1.75E-44 Residual 998 276.7649 0.27732 Total 999 336.7807 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 1.609444 0.086423 18.62288 1.15E-66 1.439853 1.779036 1.439853 1.779036 EDUC 0.090408 0.006146 14.71102 1.75E-44 0.078348 0.102468 0.078348 0.102468

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