Output from robfuel.sas
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Output from robfuel.sas |
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Bisquare Robust Regression - Fuel data 1 Iteration 1
Model: MODEL1 Dependent Variable: FUEL Fuel consumption (/person)
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 4 399316.51094 99829.12774 22.706 0.0001
Error 43 189049.96822 4396.51089
C Total 47 588366.47917
Root MSE 66.30619 R-square 0.6787
Dep Mean 576.77083 Adj R-sq 0.6488
C.V. 11.49611
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 377.291146 185.54119075 2.033 0.0482
TAX 1 -34.790149 12.97020164 -2.682 0.0103
DRIVERS 1 1336.449357 192.29814253 6.950 0.0001
ROAD 1 -0.002426 0.00338917 -0.716 0.4780
INC 1 -0.066589 0.01722175 -3.867 0.0004
Variable
Variable DF Label
INTERCEP 1 Intercept
TAX 1 Motor fuel tax (cents/gal.)
DRIVERS 1 Proportion licensed drivers
ROAD 1 Length Federal Highways (mi.)
INC 1 Per Capita Personal income ($)
Bisquare Robust Regression - Fuel data 2 Iteration 8
Model: MODEL1 Dependent Variable: FUEL Fuel consumption (/person)
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 4 167288.32727 41822.08182 35.815 0.0001
Error 40 46709.16143 1167.72904
C Total 44 213997.48870
Root MSE 34.17205 R-square 0.7817
Dep Mean 553.02626 Adj R-sq 0.7599
C.V. 6.17910
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 455.703194 108.89511896 4.185 0.0002
TAX 1 -15.457040 7.84044176 -1.971 0.0556
DRIVERS 1 934.600325 118.53860774 7.884 0.0001
ROAD 1 0.001461 0.00203350 0.718 0.4767
INC 1 -0.075185 0.00990879 -7.588 0.0001
Variable
Variable DF Label
INTERCEP 1 Intercept
TAX 1 Motor fuel tax (cents/gal.)
DRIVERS 1 Proportion licensed drivers
ROAD 1 Length Federal Highways (mi.)
INC 1 Per Capita Personal income ($)
Bisquare Robust Regression - Fuel data 3 Iteration history and parameter estimates
OBS ITER _RMSE_ INTERCEP TAX DRIVERS ROAD INC MAXDIF
1 1 66.3062 377.291 -34.7901 1336.45 -.0024259 -0.066589 0.9957 2 2 48.2139 437.749 -31.2176 1154.88 -.0016368 -0.065316 0.3940 3 3 43.7410 470.093 -28.2648 1059.45 -.0012002 -0.066819 0.1861 4 4 41.4628 485.838 -25.4150 1002.13 -.0006361 -0.069252 0.1098 5 5 40.6310 489.507 -23.2760 975.41 -.0001396 -0.071349 0.1405 6 6 37.8789 490.060 -20.3267 942.66 0.0004797 -0.073647 0.1287 7 7 34.8753 472.821 -16.8588 928.44 0.0011755 -0.075289 0.0806 8 8 34.1721 455.703 -15.4570 934.60 0.0014607 -0.075185 0.0349
Bisquare Robust Regression - Fuel data 4 Residuals, fitted values and weights
STATE FUEL _FIT_ _WEIGHT_ _RESID_ _HAT_ FLAG
AL 554 585.994 0.92065 -31.994 0.12533
AR 628 604.625 0.95724 23.375 0.09620
AZ 632 593.082 0.88375 38.918 0.09160
CA 524 539.953 0.97996 -15.953 0.10438
CO 587 604.842 0.97497 -17.842 0.10014
CT 457 435.098 0.96241 21.902 0.24269
DE 540 520.909 0.97137 19.091 0.16608
FL 574 552.080 0.96234 21.920 0.02881
GA 631 604.983 0.94716 26.017 0.07290
IA 635 585.635 0.81647 49.365 0.05927
ID 648 675.443 0.94130 -27.443 0.20116
IL 471 465.764 0.99783 5.236 0.25702
IN 580 505.923 0.61294 74.077 0.02503
KS 649 633.262 0.98050 15.738 0.14800
KY 534 513.399 0.96670 20.601 0.14889
LA 487 527.050 0.87711 -40.050 0.12100
MA 414 471.462 0.75580 -57.462 0.12906
MD 464 429.567 0.90839 34.433 0.11748
ME 541 541.656 0.99997 -0.656 0.11750
MI 525 531.921 0.99621 -6.921 0.07819
MN 566 601.957 0.90031 -35.957 0.05472
MO 603 578.295 0.95229 24.705 0.04282
MS 577 651.484 0.60920 -74.484 0.10172
MT 704 611.510 0.43768 92.490 0.02384
NC 566 552.182 0.98495 13.818 0.11339
ND 714 579.552 0.08115 134.448 0.00797
NE 640 639.444 0.99998 0.556 0.24608
NH 524 545.350 0.96426 -21.350 0.07793
NJ 467 466.606 0.99999 0.394 0.15129
NM 699 604.628 0.41946 94.372 0.04362
NV 782 602.285 0.00000 179.715 0.00000 *
NY 344 370.978 0.94324 -26.978 0.31648
OH 498 536.595 0.88561 -38.595 0.04826
OK 644 667.449 0.95696 -23.449 0.10729
OR 610 612.729 0.99941 -2.729 0.10477
PA 464 504.631 0.87364 -40.631 0.06102
RI 410 510.360 0.36183 -100.360 0.04194
SC 577 592.856 0.98021 -15.856 0.07971
SD 865 678.222 0.00000 186.778 0.00000 *
TN 571 568.040 0.99931 2.960 0.09845
TX 640 629.253 0.99088 10.747 0.33677
UT 591 544.527 0.83641 46.473 0.17240
VA 547 486.485 0.73123 60.515 0.06528
VT 561 570.385 0.99304 -9.385 0.09300
WA 510 519.477 0.99291 -9.477 0.07923
WI 508 550.169 0.86425 -42.169 0.04816
WV 460 499.213 0.88204 -39.213 0.05313
WY 968 654.581 0.00000 313.419 0.00000 *
Bisquare Robust Regression - Fuel data 5
Plot of _WEIGHT_*_RESID_. Symbol is value of STATE.
_WEIGHT_ |
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1.0 + MMI
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Residual
NOTE: 21 obs hidden.
Bisquare Robust Regression - Fuel data 6
Plot of _WEIGHT_*_HAT_. Symbol is value of STATE.
_WEIGHT_ |
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1.0 + M VTOM N NI T
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0.0 0.1 0.2 0.3 0.4
Leverage
NOTE: 6 obs hidden.