1Regression: Choosing VariablesLIR 832November 14, 2006Topics of the Day… Choosing Independent Variables What variables should be in a model?  What is the effect of leaving out important variables? What is the effect of adding in irrelevant variables? How do we decide about this? Why not just toss everything in and let our t-stats or r-square solve this for us?2Example: Effect of Unions (x) on Weekly Earnings (y)reg lnwage cbc2Source | SS df MS Number of obs = 156130-------------+------------------------------ F( 1,156128) = 3897.11Model | 1234.14281 1 1234.14281 Prob > F = 0.0000Residual | 49442.8436156128 .316681464 R-squared = 0.0244-------------+------------------------------ Adj R-squared = 0.0243Total | 50676.9864156129 .324584071 Root MSE = .56274------------------------------------------------------------------------------lnwage3 | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+----------------------------------------------------------------cbc2 | .2488057 .0039856 62.43 0.000 .2409941 .2566173_cons | 2.469369 .001545 1598.30 0.000 2.466341 2.472397------------------------------------------------------------------------------Example: Effect of Unions (x) on Weekly Earnings (y)reg lnwage cbc2 ageSource | SS df MS Number of obs = 156130-------------+------------------------------ F( 2,156127) = 7530.01Model | 4458.26229 2 2229.13115 Prob > F = 0.0000Residual | 46218.7241156127 .296032871 R-squared = 0.0880-------------+------------------------------ Adj R-squared = 0.0880Total | 50676.9864156129 .324584071 Root MSE = .54409------------------------------------------------------------------------------lnwage3 | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+----------------------------------------------------------------cbc2 | .2014921 .00388 51.93 0.000 .1938874 .2090969age | .0111539 .0001069 104.36 0.000 .0109444 .0113634_cons | 2.043437 .0043461 470.17 0.000 2.034918 2.051955------------------------------------------------------------------------------3reg lnwage cbc2 age female married black other NE Midwest South city1mil ed3 ed4 aa ed6 ed7Source | SS df MS Number of obs = 156130-------------+------------------------------ F( 15,156114) = 5888.11Model | 18311.0587 15 1220.73725 Prob > F = 0.0000Residual | 32365.9277156114 .20732239 R-squared = 0.3613-------------+------------------------------ Adj R-squared = 0.3613Total | 50676.9864156129 .324584071 Root MSE = .45533------------------------------------------------------------------------------lnwage3 | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+----------------------------------------------------------------cbc2 | .1360972 .0032913 41.35 0.000 .1296462 .1425481age | .0067085 .000096 69.85 0.000 .0065203 .0068968female | -.2151269 .002322 -92.65 0.000 -.2196779 -.2105759married | .127496 .0025106 50.78 0.000 .1225752 .1324168black | -.0645881 .0039931 -16.17 0.000 -.0724145 -.0567617other | -.0454844 .0052715 -8.63 0.000 -.0558164 -.0351524NE | .0089504 .0034877 2.57 0.010 .0021146 .0157862Midwest | -.0148798 .0033238 -4.48 0.000 -.0213944 -.0083653South | -.0260961 .0032539 -8.02 0.000 -.0324736 -.0197186city1mil | .1118365 .0023835 46.92 0.000 .1071648 .1165081ed3 | .2875855 .0038465 74.77 0.000 .2800464 .2951246ed4 | .3676268 .0041132 89.38 0.000 .359565 .3756885aa | .4949227 .0050869 97.29 0.000 .4849525 .5048929ed6 | .7416187 .0042642 173.92 0.000 .7332609 .7499764ed7 | .896922 .005259 170.55 0.000 .8866146 .9072295_cons | 1.813933 .0050728 357.58 0.000 1.803991 1.823876------------------------------------------------------------------------------reg lnwage cbc2 age female married black other NE Midwest South city1mil ed3 ed4aa ed6 ed7 managerprof tech sales privhh protect servocc servocc farmer craft oper transop laborerSource | SS df MS Number of obs = 156130-------------+------------------------------ F( 27,156102) = 4558.99Model | 22342.7173 27 827.508049 Prob > F = 0.0000Residual | 28334.2691156102 .181511249 R-squared = 0.4409-------------+------------------------------ Adj R-squared = 0.4408Total | 50676.9864156129 .324584071 Root MSE = .42604------------------------------------------------------------------------------lnwage3 | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+----------------------------------------------------------------cbc2 | .1348609 .0031501 42.81 0.000 .1286866 .1410351age | .0056959 .0000906 62.84 0.000 .0055183 .0058736female | -.1960792 .0023927 -81.95 0.000 -.2007688 -.1913895married | .0945142 .0023617 40.02 0.000 .0898854 .0991431black | -.0497951 .0037475 -13.29 0.000 -.05714 -.0424501other | -.0287192 .0049378 -5.82 0.000 -.0383971 -.0190413NE | .0106994 .0032661 3.28 0.001 .0042979 .0171009Midwest | -.0160232 .0031147 -5.14 0.000 -.0221278 -.0099185South | -.0345 .003048 -11.32 0.000 -.040474 -.028526city1mil | .1006931 .0022359 45.04 0.000 .0963108 .1050754ed3 | .2163545 .0036596 59.12 0.000 .2091817 .2235273ed4 | .2570192 .0039814 64.55 0.000 .2492157 .2648228aa | .3307331 .0049498 66.82 0.000 .3210316 .3404345ed6 | .5085537 .004477 113.59 0.000 .4997789 .5173285ed7 | .6125842 .0056601 108.23 0.000 .6014905 .6236779manager | .3553568 .0039626 89.68 0.000 .3475901 .3631235prof | .2786787 .0041472 67.20 0.000 .2705503 .2868071tech | .2750721 .0062083 44.31 0.000 .262904 .2872401sales | .0288982 .0040054 7.21 0.000 .0210478 .0367487privhh | -.3069562 .0139645 -21.98 0.000 -.3343264 -.2795861protect | .0610202 .0081706 7.47 0.000 .045006