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 = 0.0000
Residual | 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/hprice2
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 = 0.0000
Residual | 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 = 0.0000
Residual | 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 = 0.0474
Residual | 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 = 0.0000
Residual | 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]*10
7.014077
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