C3D2 - GRAPHING A RELATIONSHIP IN A MULTIPLE REGRESSION...

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Unformatted text preview: GRAPHING A RELATIONSHIP IN A MULTIPLE REGRESSION MODEL . reg EARNINGS S EXP Source | SS df MS Number of obs = 540-------------+------------------------------ F( 2, 537) = 67.54 Model | 22513.6473 2 11256.8237 Prob > F = 0.0000 Residual | 89496.5838 537 166.660305 R-squared = 0.2010-------------+------------------------------ Adj R-squared = 0.1980 Total | 112010.231 539 207.811189 Root MSE = 12.91------------------------------------------------------------------------------ EARNINGS | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- S | 2.678125 .2336497 11.46 0.000 2.219146 3.137105 EXP | .5624326 .1285136 4.38 0.000 .3099816 .8148837 _cons | -26.48501 4.27251 -6.20 0.000 -34.87789 -18.09213------------------------------------------------------------------------------ The output above shows the result of regressing EARNINGS , hourly earnings in dollars, on S , years of schooling, and EXP , years of work experience. 1 EXP S INGS N EAR 56 . 68 . 2 49 . 26 + +- = GRAPHING A RELATIONSHIP IN A MULTIPLE REGRESSION MODEL 2 Suppose that you were particularly interested in the relationship between EARNINGS and S and wished to represent it graphically, using the sample data.-20 20 40 60 80 100 120 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Years of schooling Hourly earnings ($) GRAPHING A RELATIONSHIP IN A MULTIPLE REGRESSION MODEL 3 A simple plot would be misleading.-20 20 40 60 80 100 120 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Years of schooling Hourly earnings ($)-20 20 40 60 80 100 120 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Years of schooling Hourly earnings ($) GRAPHING A RELATIONSHIP IN A MULTIPLE REGRESSION MODEL 4 Schooling is negatively correlated with work experience. The plot fails to take account of this, and as a consequence the regression line underestimates the impact of schooling on earnings. . cor S EXP (obs=540) | S ASVABC--------+------------------ S| 1.0000 EXP| -0.2179 1.0000-20 20 40 60 80 100 120 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Years of schooling Hourly earnings ($) GRAPHING A RELATIONSHIP IN A MULTIPLE REGRESSION MODEL 5 . cor S EXP (obs=540) | S ASVABC--------+------------------ S| 1.0000 EXP| -0.2179 1.0000 We will investigate the distortion mathematically when we come to omitted variable bias.-20 20 40 60 80 100 120 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Years of schooling Hourly earnings ($) GRAPHING A RELATIONSHIP IN A MULTIPLE REGRESSION MODEL 6 . cor S EXP (obs=540) | S ASVABC--------+------------------ S| 1.0000 EXP| -0.2179 1.0000 To eliminate the distortion, you purge both EARNINGS and S of their components related to EXP and then draw a scatter diagram using the purged variables. . reg EARNINGS EXP....
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This note was uploaded on 02/08/2011 for the course ECON 101 taught by Professor Gilbert during the Spring '11 term at Bryan College.

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C3D2 - GRAPHING A RELATIONSHIP IN A MULTIPLE REGRESSION...

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