Source |
SS df
MS
Number of obs = 51
---------+------------------------------
F( 5, 45) = 14.94
Model | 1973.30839
5 394.661678
Prob > F = 0.0000
Residual | 1188.64143
45 26.414254
R-squared = 0.6241
---------+------------------------------
Adj R-squared = 0.5823
Total | 3161.94982
50 63.2389964
Root MSE = 5.1395
------------------------------------------------------------------------------
grad |
Coef. Std. Err. t
P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
inc |
.001785 .0008021 2.225
0.031 .0001695 .0034005
pbla | -.4141165
.062532 -6.622 0.000
-.5400623 -.2881706
phis | -.4073045
.1169389 -3.483 0.001
-.6428316 -.1717774
edexp | -.0013187
.0013975 -0.944 0.350
-.0041334 .0014961
urb |
-.1083125 .0460315 -2.353
0.023 -.2010247 -.0156004
_cons | 69.04199
5.372707 12.851 0.000
58.2208 79.86317
* qreg performs least absolute residuals
or minimum L1-norm regression
. qreg grad inc pbla phis edexp
urb
Iteration 1: WLS sum of
weighted deviations = 208.54367
Iteration 1: sum of abs. weighted
deviations = 236.21414
Iteration 2: sum of abs. weighted
deviations = 207.28992
Iteration 3: sum of abs. weighted
deviations = 201.05331
Iteration 4: sum of abs. weighted
deviations = 200.34445
Iteration 5: sum of abs. weighted
deviations = 199.84208
Median regression
Number of obs = 51
Raw sum of deviations
312.5 (about 74.699997)
Min sum of deviations 199.8421
Pseudo R2 = 0.3605
------------------------------------------------------------------------------
grad |
Coef. Std. Err. t
P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
inc |
.0029724 .0015524 1.915
0.062 -.0001544 .0060992
pbla | -.3728657
.10048 -3.711 0.001
-.5752429 -.1704885
phis | -.4282676
.2360359 -1.814 0.076
-.9036684 .0471332
edexp | -.0028488
.002912 -0.978 0.333
-.0087138 .0030162
urb |
-.189569 .0949354 -1.997
0.052 -.3807787 .0016407
_cons | 65.07659
9.923346 6.558 0.000
45.08995 85.06324
* rreg performs robust regression
using iteratively reweighted least squares with Huber and biweight functions
tuned for 95% percent efficiency.
. rreg grad inc pbla phis edexp
urb
Huber iteration 1:
maximum difference in weights = .12234393
Huber iteration 2:
maximum difference in weights = .05382205
Huber iteration 3:
maximum difference in weights = .02203892
Biweight iteration 4: maximum
difference in weights = .1559363
Biweight iteration 5: maximum
difference in weights = .01087629
Biweight iteration 6: maximum
difference in weights = .00265105
Robust regression estimates
Number of obs = 50
F( 5, 44) = 15.88
Prob > F = 0.0000
------------------------------------------------------------------------------
grad |
Coef. Std. Err. t
P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
inc |
.0023026 .0008351 2.757
0.008 .0006196 .0039857
pbla | -.4363851
.0646035 -6.755 0.000
-.5665848 -.3061854
phis | -.7694453
.1837624 -4.187 0.000
-1.139794 -.3990965
edexp | -.0020356
.0014493 -1.405 0.167
-.0049566 .0008853
urb |
-.0876499 .0483629 -1.812
0.077 -.1851189 .0098191
_cons | 65.19619
5.641651 11.556 0.000
53.82619 76.56619
* The option tune(6), using a tuning
constant of 6, down-weights outliers more steeply than the default 7.
. rreg grad inc pbla phis edexp
urb, tune(6)
Huber iteration 1:
maximum difference in weights = .12234393
Huber iteration 2:
maximum difference in weights = .05382205
Huber iteration 3:
maximum difference in weights = .02203892
Biweight iteration 4: maximum
difference in weights = .21024998
Biweight iteration 5: maximum
difference in weights = .02216084
Biweight iteration 6: maximum
difference in weights = .00613242
Robust regression estimates
Number of obs = 50
F( 5, 44) = 14.70
Prob > F = 0.0000
------------------------------------------------------------------------------
grad |
Coef. Std. Err. t
P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
inc |
.0023658 .0008732 2.709
0.010 .0006061 .0041255
pbla | -.4360197
.0675471 -6.455 0.000
-.5721519 -.2998875
phis | -.7707839
.1921354 -4.012 0.000
-1.158007 -.3835604
edexp | -.0020797
.0015154 -1.372 0.177
-.0051338 .0009743
urb |
-.0919598 .0505665 -1.819
0.076 -.1938699 .0099503
_cons | 64.86228
5.898709 10.996 0.000
52.97421 76.75035
------------------------------------------------------------------------------
* In Stata 6, I [Cheol-Sung Lee]
could not find the relevant commands for robust regressions using Bisquare,
Hampel, Trim, T method and Hadi method; I will check higher versions.