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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_ | | 1.0 + MMI | NC DA | IO G | MA M | L A | W | I 0.8 + | | M V | | | | 0.6 + M I | | | | | | M 0.4 + | R | | | | | 0.2 + | | | | N | | 0.0 + NS W | --+------------+------------+------------+------------+------------+- -100 0 100 200 300 400 Residual NOTE: 21 obs hidden.
Bisquare Robust Regression - Fuel data 6
Plot of _WEIGHT_*_HAT_. Symbol is value of STATE. _WEIGHT_ | | 1.0 + M VTOM N NI T | F N ACN K D C | M G O I N | M MA | OWP A L | W | I U 0.8 + | | V M | | | | 0.6 + I M | | | | | | M N 0.4 + | R | | | | | 0.2 + | | | | N | | 0.0 + N | ---+------------+------------+------------+------------+-- 0.0 0.1 0.2 0.3 0.4 Leverage NOTE: 6 obs hidden.