OPTIONS LS=72;
TITLE 'EXAMPLE 15. ROBUST REGRESSION: US POPULATION DATA';
DATA USPOP;
INPUT YEAR POP;
CARDS;
1790       3.929
1800       5.308
1810       7.239
1820       9.638
1830      12.866
1840      17.069
1850      23.191
1860      31.443
1870      39.818
1880      50.155
1890      62.947
1900      75.994
1910      91.972
1920     105.710
1930     122.775
1940     131.669
1950     151.325
1960     179.323
1970     203.211
;
PROC NLIN DATA=USPOP NOHALVE;
PARMS B0=20450.43  B1=-22.7806  B2=.0063456;
MODEL POP=B0+B1*YEAR+B2*YEAR*YEAR;
DER.B0=1;
DER.B1=YEAR;
DER.B2=YEAR*YEAR;
RESID=POP-MODEL.POP;
SIGMA=2;
B=4.685;
R=ABS(RESID/SIGMA);
IF R<=B THEN _WEIGHT_=(1-(R/B)**2)**2;
ELSE _WEIGHT_=0;
OUTPUT OUT=C  R=RBI;
RUN;
DATA C;
SET C;
SIGMA=2;
B=4.685;
R=ABS(RBI/SIGMA);
IF R<=B THEN _WEIGHT_=(1-(R/B)**2)**2;
ELSE _WEIGHT_=0;
RUN;
PROC PRINT;
RUN;