Chapter 6 - Multiple Regression Analysis Further Issues

发布时间：2024-10-30

Stata Textbook Examples

Introductory Econometrics: A Modern Approach by Jeffrey M. Wooldridge (1st & 2nd eds.)

Chapter 6 - Multiple Regression Analysis: Further Issues

Example 6.1: Effect of Pollution on Housing Prices

use http://fmwww.bc.edu/ec-p/data/wooldridge/HPRICE2

reg price nox crime rooms dist stratio, beta

Source | SS df MS Number of obs = 506---------+------------------------------ F( 5, 500) = 174.47 Model | 2.7223e+10 5 5.4445e+09 Prob > F = 0.0000Residual | 1.5603e+10 500 31205611.6 R-squared = 0.6357---------+------------------------------ Adj R-squared = 0.6320 Total | 4.2826e+10 505 84803032.0 Root MSE = 5586.2------------------------------------------------------------------------------ price | Coef. Std. Err. t P>|t| Beta---------+-------------------------------------------------------------------- nox | -2706.433 354.0869 -7.643 0.000 -.340446 crime | -153.601 32.92883 -4.665 0.000 -.1432828 rooms | 6735.498 393.6037 17.112 0.000 .5138878 dist | -1026.806 188.1079 -5.459 0.000 -.2348385 stratio | -1149.204 127.4287 -9.018 0.000 -.2702799 _cons | 20871.13 5054.599 4.129 0.000 .------------------------------------------------------------------------------

Example 6.2: Effect of Pollution on Housing Prices

use http://fmwww.bc.edu/ec-p/data/wooldridge/PRICE2

gen rooms2=rooms*rooms

gen ldist=log(dist)

reg lprice lnox ldist rooms rooms2 stratio

Source | SS df MS Number of obs = 506---------+------------------------------ F( 5, 500) = 151.77 Model | 50.98725 5 10.19745 Prob > F = 0.0000Residual | 33.595021 500 .067190042 R-squared = 0.6028---------+------------------------------ Adj R-squared = 0.5988 Total | 84.5822709 505 .167489645 Root MSE = .25921

------------------------------------------------------------------------------ lprice | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------+-------------------------------------------------------------------- lnox | -.9016832 .114687 -7.862 0.000 -1.127011 -.6763553 ldist | -.0867821 .0432808 -2.005 0.045 -.1718166 -.0017475 rooms | -.5451122 .1654542 -3.295 0.001 -.8701834 -.220041 rooms2 | .0622611 .012805 4.862 0.000 .0371029 .0874194 stratio | -.0475903 .0058542 -8.129 0.000 -.0590921 -.0360884 _cons | 13.38548 .5664734 23.629 0.000 12.27252 14.49844------------------------------------------------------------------------------

Turnaround value of rooms

display -1*_b[rooms]/(2*_b[rooms2])

4.3776278

Change in price if rooms increases from 5 to 6

display 100*(_b[rooms]+2*_b[rooms2]*5)

7.7499207

Change in price if rooms increases from 6 to 7

display 100*(_b[rooms]+2*_b[rooms2]*6)

20.202149

Example 6.3: Effect of Attendance on Final Exam Performance

use http://fmwww.bc.edu/ec-p/data/wooldridge/ATTEND

summ priGPA

Variable | Obs Mean Std. Dev. Min Max

---------+-----------------------------------------------------

priGPA | 680 2.586775 .5447141 .857 3.93

gen priGPA2=priGPA*priGPA

gen ACT2=ACT*ACT

gen priatn=priGPA*atndrte

reg stndfnl atndrte priGPA ACT priGPA2 ACT2 priatn

Source | SS df MS Number of obs = 680

---------+------------------------------ F( 6, 673) = 33.25 Model | 152.001001 6 25.3335002 Prob > F = 0.0000Residual | 512.76244 673 .761905557 R-squared = 0.2287---------+------------------------------ Adj R-squared = 0.2218 Total | 664.763441 679 .97903305 Root MSE = .87287------------------------------------------------------------------------------ stndfnl | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------+-------------------------------------------------------------------- atndrte | -.0067129 .0102321 -0.656 0.512 -.0268035 .0133777 priGPA | -1.62854 .4810025 -3.386 0.001 -2.572986 -.6840938 ACT | -.1280394 .098492 -1.300 0.194 -.3214279 .0653492 priGPA2 | .2959046 .1010495 2.928 0.004 .0974945 .4943147 ACT2 | .0045334 .0021764 2.083 0.038 .00026 .0088068 priatn | .0055859 .0043174 1.294 0.196 -.0028913 .0140631 _cons | 2.050293 1.360319 1.507 0.132 -.6206864 4.721272------------------------------------------------------------------------------

Partial effect of atndrte on stndfnl

display _b[atndrte]+_b[priatn]*2.59

.00775457

Example 6.4: CEO Compensation and Firm Performance

use http://fmwww.bc.edu/ec-p/data/wooldridge/CEOSAL

reg salary sales roe

Source | SS df MS Number of obs = 209---------+------------------------------ F( 2, 206) = 3.09 Model | 11427511.8 2 5713755.89 Prob > F = 0.0474Residual | 380305470 206 1846143.06 R-squared = 0.0292---------+------------------------------ Adj R-squared = 0.0197 Total | 391732982 208 1883331.64 Root MSE = 1358.7------------------------------------------------------------------------------ salary | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------+-------------------------------------------------------------------- sales | .0163416 .0088736 1.842 0.067 -.0011532 .0338363 roe | 19.63097 11.07655 1.772 0.078 -2.20697 41.46891 _cons | 830.6313 223.9049 3.710 0.000 389.1924 1272.07------------------------------------------------------------------------------reg lsalary lsales roe

Source | SS df MS Number of obs = 209---------+------------------------------ F( 2, 206) = 40.45 Model | 18.8149023 2 9.40745113 Prob > F = 0.0000Residual | 47.9072676 206 .232559552 R-squared = 0.2820---------+------------------------------ Adj R-squared = 0.2750 Total | 66.7221699 208 .320779663 Root MSE = .48224------------------------------------------------------------------------------ lsalary | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------+-------------------------------------------------------------------- lsales | .2750875 .033254 8.272 0.000 .2095258 .3406492 roe | .0178723 .0039551 4.519 0.000 .0100746 .0256699 _cons | 4.362167 .2938776 14.843 0.000 3.782774 4.941561------------------------------------------------------------------------------

Example 6.5: Confidence Interval for Predicted College GPA (Approach in Book)

use http://fmwww.bc.edu/ec-p/data/wooldridge/GPA2

gen hsize2=hsize*hsize

reg colgpa sat hsperc hsize hsize2

Source | SS df MS Number of obs = 4137-------------+------------------------------ F( 4, 4132) = 398.02 Model | 499.030504 4 124.757626 Prob > F = 0.0000 Residual | 1295.16517 4132 .313447524 R-squared = 0.2781-------------+------------------------------ Adj R-squared = 0.2774 Total | 1794.19567 4136 .433799728 Root MSE = .55986------------------------------------------------------------------------------ colgpa | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- sat | .0014925 .0000652 22.89 0.000 .0013646 .0016204 hsperc | -.0138558 .000561 -24.70 0.000 -.0149557 -.0127559 hsize | -.0608815 .0165012 -3.69 0.000 -.0932327 -.0285302 hsize2 | .0054603 .0022698 2.41 0.016 .0010102 .0099104 _cons | 1.492652 .0753414 19.81 0.000 1.344942 1.640362------------------------------------------------------------------------------

Predicted college GPA

display _b[_cons]+_b[sat]*1200+_b[hsperc]*30+_b[hsize]*5+_b[hsize2]*25

2.7000755

gen sat0=sat-1200

gen hsperc0=hsperc-30

gen hsize0=hsize-5

gen hsize20=hsize2-25

reg colgpa sat0 hsperc0 hsize0 hsize20

Source | SS df MS Number of obs = 4137-------------+------------------------------ F( 4, 4132) = 398.02 Model | 499.030503 4 124.757626 Prob > F = 0.0000 Residual | 1295.16517 4132 .313447524 R-squared = 0.2781-------------+------------------------------ Adj R-squared = 0.2774 Total | 1794.19567 4136 .433799728 Root MSE = .55986------------------------------------------------------------------------------ colgpa | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- sat0 | .0014925 .0000652 22.89 0.000 .0013646 .0016204 hsperc0 | -.0138558 .000561 -24.70 0.000 -.0149557 -.0127559 hsize0 | -.0608815 .0165012 -3.69 0.000 -.0932327 -.0285302 hsize20 | .0054603 .0022698 2.41 0.016 .0010102 .0099104 _cons | 2.700075 .0198778 135.83 0.000 2.661104 2.739047------------------------------------------------------------------------------

Example 6.5: Confidence Interval for Predicted College GPA (Another Approach)

use http://fmwww.bc.edu/ec-p/data/wooldridge/GPA2

gen hsize2=hsize*hsize

reg colgpa sat hsperc hsize hsize2

Source | SS df MS Number of obs = 4137-------------+------------------------------ F( 4, 4132) = 398.02 Model | 499.030504 4 124.757626 Prob > F = 0.0000 Residual | 1295.16517 4132 .313447524 R-squared = 0.2781-------------+------------------------------ Adj R-squared = 0.2774 Total | 1794.19567 4136 .433799728 Root MSE = .55986------------------------------------------------------------------------------ colgpa | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+---------------------------------------------------------------- sat | .0014925 .0000652 22.89 0.000 .0013646 .0016204 hsperc | -.0138558 .000561 -24.70 0.000 -.0149557 -.0127559 hsize | -.0608815 .0165012 -3.69 0.000 -.0932327 -.0285302 hsize2 | .0054603 .0022698 2.41 0.016 .0010102 .0099104 _cons | 1.492652 .0753414 19.81 0.000 1.344942 1.640362------------------------------------------------------------------------------set obs 4138

replace sat=1200 in 4138/4138

replace hsperc=30 in 4138/4138

replace hsize=5 in 4138/4138

replace hsize2=25 in 4138/4138

regress

Source | SS df MS Number of obs = 4137-------------+------------------------------ F( 4, 4132) = 398.02 Model | 499.030504 4 124.757626 Prob > F = 0.0000 Residual | 1295.16517 4132 .313447524 R-squared = 0.2781-------------+------------------------------ Adj R-squared = 0.2774 Total | 1794.19567 4136 .433799728 Root MSE = .55986------------------------------------------------------------------------------ colgpa | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- sat | .0014925 .0000652 22.89 0.000 .0013646 .0016204 hsperc | -.0138558 .000561 -24.70 0.000 -.0149557 -.0127559 hsize | -.0608815 .0165012 -3.69 0.000 -.0932327 -.0285302 hsize2 | .0054603 .0022698 2.41 0.016 .0010102 .0099104 _cons | 1.492652 .0753414 19.81 0.000 1.344942 1.640362------------------------------------------------------------------------------predict colgpahat in 4138/4138,stdp

predict colgpahatt in 4138/4138,xb

gen lb = colgpahatt-1.96* colgpahat in 4138/4138

gen ub = colgpahatt+1.96* colgpahat in 4138/4138

list colgpahat lb colgpahatt ub in 4138/4138

colgpahat lb colgpahatt ub

4138. .0198778 2.661115 2.700075 2.739036

Example 6.6: Confidence Interval for Future College GPA

use http://fmwww.bc.edu/ec-p/data/wooldridge/GPA2

gen hsize2=hsize*hsize

reg colgpa sat hsperc hsize hsize2

Source | SS df MS Number of obs = 4137-------------+------------------------------ F( 4, 4132) = 398.02 Model | 499.030504 4 124.757626 Prob > F = 0.0000 Residual | 1295.16517 4132 .313447524 R-squared = 0.2781-------------+------------------------------ Adj R-squared = 0.2774 Total | 1794.19567 4136 .433799728 Root MSE = .55986------------------------------------------------------------------------------ colgpa | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- sat | .0014925 .0000652 22.89 0.000 .0013646 .0016204 hsperc | -.0138558 .000561 -24.70 0.000 -.0149557 -.0127559 hsize | -.0608815 .0165012 -3.69 0.000 -.0932327 -.0285302 hsize2 | .0054603 .0022698 2.41 0.016 .0010102 .0099104 _cons | 1.492652 .0753414 19.81 0.000 1.344942 1.640362------------------------------------------------------------------------------set obs 4138

replace sat=1200 in 4138/4138

replace hsperc=30 in 4138/4138

replace hsize=5 in 4138/4138

replace hsize2=25 in 4138/4138

regress

Source | SS df MS Number of obs = 4137-------------+------------------------------ F( 4, 4132) = 398.02 Model | 499.030504 4 124.757626 Prob > F = 0.0000

Residual | 1295.16517 4132 .313447524 R-squared = 0.2781-------------+------------------------------ Adj R-squared = 0.2774 Total | 1794.19567 4136 .433799728 Root MSE = .55986------------------------------------------------------------------------------ colgpa | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- sat | .0014925 .0000652 22.89 0.000 .0013646 .0016204 hsperc | -.0138558 .000561 -24.70 0.000 -.0149557 -.0127559 hsize | -.0608815 .0165012 -3.69 0.000 -.0932327 -.0285302 hsize2 | .0054603 .0022698 2.41 0.016 .0010102 .0099104 _cons | 1.492652 .0753414 19.81 0.000 1.344942 1.640362------------------------------------------------------------------------------predict cc in 4138/4138,stdf

predict colgpahatt in 4138/4138,xb

gen lb1 = colgpahatt-1.96* cc in 4138/4138

gen ub1 = colgpahatt+1.96* cc in 4138/4138

list cc lb1 colgpahatt ub1 in 4138/4138

cc lb1 colgpahatt ub1

4138. .5602166 1.602051 2.700075 3.7981

Example 6.7: Predicting CEO Salaries

use http://fmwww.bc.edu/ec-p/data/wooldridge/CEOSAL2

reg lsalary lsales lmktval ceoten

Source | SS df MS Number of obs = 177-------------+------------------------------ F( 3, 173) = 26.91 Model | 20.5672427 3 6.85574758 Prob > F = 0.0000 Residual | 44.0789788 173 .254791785 R-squared = 0.3182-------------+------------------------------ Adj R-squared = 0.3063 Total | 64.6462215 176 .367308077 Root MSE = .50477------------------------------------------------------------------------------ lsalary | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- lsales | .1628544 .0392421 4.15 0.000 .0853995 .2403094 lmktval | .109243 .0495947 2.20 0.029 .0113545 .2071315

ceoten | .0117054 .0053261 2.20 0.029 .001193 .0222178 _cons | 4.503795 .2572344 17.51 0.000 3.996073 5.011517------------------------------------------------------------------------------predict lsal, xb

gen mhat=exp(lsal)

Predicted salary

display _b[_cons]+_b[lsales]*log(5000)+_b[lmktval]*log(10000)+_b[ceoten]*107.014077

reg salary mhat, noconstant

Source | SS df MS Number of obs = 177-------------+------------------------------ F( 1, 176) = 562.39 Model | 147352712 1 147352712 Prob > F = 0.0000 Residual | 46113900.4 176 262010.798 R-squared = 0.7616-------------+------------------------------ Adj R-squared = 0.7603 Total | 193466612 177 1093031.71 Root MSE = 511.87------------------------------------------------------------------------------ salary | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- mhat | 1.116857 .0470953 23.71 0.000 1.023912 1.209801------------------------------------------------------------------------------

Predicted salary

display _b[mhat]*exp(7.013)

1240.9674

Example 6.8: Predicting CEO Salaries

use http://fmwww.bc.edu/ec-p/data/wooldridge/CEOSAL2

reg salary sales mktval ceoten

Source | SS df MS Number of obs = 177-------------+------------------------------ F( 3, 173) = 14.53 Model | 12230632.6 3 4076877.52 Prob > F = 0.0000 Residual | 48535332.2 173 280551.053 R-squared = 0.2013-------------+------------------------------ Adj R-squared = 0.1874

Total | 60765964.7 176 345261.163 Root MSE = 529.67------------------------------------------------------------------------------ salary | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- sales | .0190191 .0100561 1.89 0.060 -.0008294 .0388676 mktval | .0234003 .0094826 2.47 0.015 .0046839 .0421167 ceoten | 12.70337 5.618052 2.26 0.025 1.614616 23.79211 _cons | 613.4361 65.23685 9.40 0.000 484.6735 742.1987------------------------------------------------------------------------------This page prepared by Oleksandr Talavera (revised 8 Nov 2002)

Send your questions/comments/suggestions to Kit Baum at baum@bc.edu

These pages are maintained by the Faculty Micro Resource Center's GSA Program,

a unit of Boston College Academic Technology Services

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