*#D7     EXHIBIT 27 -                                      IX27SIM.SAS ;
  OPTIONS PAGENO=1 PS=65 S=77 LS=77 CENTER NODATE FORMDLIM='' ;
  TITLE1 ' DEMONSTRATION OF STATISTICAL CONCEPTS VIA SIMULATION';
 %LET NSAMPLES = 10000 ;
 %LET M9=40; %LET M10=47 ; %LET M11=56; %LET M12=64 ;
 *NOTE THAT IN EXHIBIT 26 MODEL 3 IS TRUE.
  IN EXHIBIT 27 MODEL 3 IS NOT TRUE - DIFFERENCES NOT CONSTANT ;
 %LET SEED = 7831349 ;
 %LET SIGMA = 10 ;
 %LET NPERCELL = 5 ;
 %LET M1_DF = %EVAL(4*(&NPERCELL-1));
 %LET M3_DF = %EVAL(4*&NPERCELL-2) ;
 %LET TOBS = %EVAL(&NPERCELL*4*&NSAMPLES) ;
  TITLE2 " EXPECTED VALUES ARE &M9, &M10, &M11, AND &M12 ";
DATA T1; LENGTH  G Y X9 X10 X11 X12 U 3;
         DO SAMPLE = 1 TO &NSAMPLES ;
         DO G = 9 TO 12 ; DO N = 1 TO &NPERCELL ;
         X9 = 0; X10 = 0; X11 = 0; X12 = 0;
         IF G EQ 9 THEN X9  = 1 ;
    ELSE IF G EQ 10 THEN X10 = 1 ;
    ELSE IF G EQ 11 THEN X11 = 1 ;
    ELSE IF G EQ 12 THEN X12 = 1 ; U = 1 ;
 EV = &M9*X9 + &M10*X10 + &M11*X11 + &M12*X12 ;
 EPSILON = RANNOR(&SEED)*&SIGMA ;
 Y1 = EV + EPSILON ; Y = ROUND(Y1) ;
 DROP N ; OUTPUT ;
  END ; * OF N LOOP ; END; * OF G LOOP; END ; * OF SAMPLE LOOP; RUN;
PROC PRINT DATA=T1(OBS=40) ;
 TITLE3 "FIRST 40 (OF &TOBS) OBSERVATIONS OF SIMULATED DATA";
  RUN ;
OPTIONS NONOTES ; * TO KEEP CLUTTER OUT OF LOG ;
PROC REG DATA = T1 OUTEST = WTS ADJRSQ NOPRINT ; BY SAMPLE ;
  MODEL_1: MODEL Y = X9-X12 / NOINT ;
  MODEL_2: MODEL Y = U / NOINT ;
  MODEL_3: MODEL Y = U G / NOINT ;
RUN ;
OPTIONS NOTES ;
 /*
PROC PRINT DATA=WTS(OBS=40 DROP = _TYPE_ _DEPVAR_ INTERCEP
                   _IN_ _P_ _EDF_ _ADJRSQ_) Y ;
 TITLE2 ' WTS FILE PRODUCED BY PROC REG ' ;  RUN ;
 */
 DATA SUMRY;
  RETAIN M1_PV_9 M1_PV_10 M1_PV_11 M1_PV_12 B0_2 B0_3 B1
         M3_PV_9 M3_PV_10 M3_PV_11 M3_PV_12 ASE_1 - ASE_3
         S1-S3 V1-V3  F12 F13 F32 P12 P13 P32
         PR12_05 PR12_01 PR13_05 PR13_01 PR32_05 PR32_01
         R1-R3 ;
  KEEP   M1_PV_9 M1_PV_10 M1_PV_11 M1_PV_12 B0_2 B0_3 B1
         M3_PV_9 M3_PV_10 M3_PV_11 M3_PV_12 ASE_1 - ASE_3
         S1-S3 V1-V3  F12 F13 F32 P12 P13 P32 SAMPLE
         PR12_05 PR12_01 PR13_05 PR13_01 PR32_05 PR32_01;
  SET WTS ; IF _MODEL_ EQ 'MODEL_1' THEN DO ;
  R1=_RSQ_ ;
  M1_PV_9 = X9; M1_PV_10 = X10; M1_PV_11= X11; M1_PV_12= X12;
  S1 = _RMSE_ ; V1 = S1*S1 ;
  ASE_1 =((X9-&M9)*(X9-&M9)+(X10-&M10)*(X10-&M10)+
         (X11-&M11)*(X11-&M11)+(X12-&M12)*(X12-&M12))/4 ; END;
        ELSE IF _MODEL_ EQ 'MODEL_2' THEN DO ;
  R2 = _RSQ_ ; F12 = ((R1-R2)/3) / ((1-R1)/&M1_DF) ;
  B0_2 = U ; S2 = _RMSE_ ; V2 = S2*S2 ;
  P12 = 1 - PROBF(F12,3,&M1_DF,0.) ;
  IF P12 LT .05 THEN PR12_05 = 1. ; ELSE PR12_05 = 0 ;
  IF P12 LT .01 THEN PR12_01 = 1. ; ELSE PR12_01 = 0 ;
  ASE_2 =((U-&M9)*(U-&M9)+(U-&M10)*(U-&M10)+(U-&M11)*(U-&M11)+
         (U-&M12)*(U-&M12))/4 ;          END;
        ELSE IF _MODEL_ EQ 'MODEL_3' THEN DO ;
  R3 = _RSQ_ ; B0_3 = U ; B1=G ; S3 = _RMSE_ ; V3 = S3*S3 ;
  M3_PV_9 = U + 9*G ;  M3_PV_10 = U +10*G ;
  M3_PV_11 = U +11*G ;  M3_PV_12 = U +12*G ;
  F13 = ((R1-R3)/2) / ((1-R1) / &M1_DF) ;
  F32 = (R3-R2) / ((1-R3)/&M3_DF) ;
  P13 = 1 - PROBF(F13,2,&M1_DF,0.) ; P32 = 1-PROBF(F32,1,&M3_DF,0.) ;
  IF P13 LT .05 THEN PR13_05 = 1. ; ELSE PR13_05 = 0 ;
  IF P13 LT .01 THEN PR13_01 = 1. ; ELSE PR13_01 = 0 ;
  IF P32 LT .05 THEN PR32_05 = 1. ; ELSE PR32_05 = 0 ;
  IF P32 LT .01 THEN PR32_01 = 1. ; ELSE PR32_01 = 0 ;

  ASE_3 =((M3_PV_9-&M9)*(M3_PV_9-&M9)+ (M3_PV_10-&M10)*(M3_PV_10-&M10)
  + (M3_PV_11-&M11)*(M3_PV_11-&M11)
  + (M3_PV_12-&M12)*(M3_PV_12-&M12)) / 4 ;
                  OUTPUT ; END ; RETURN ; RUN ;
  PROC PRINT DATA=SUMRY(OBS=10) NOOBS;
  TITLE1 "SUMMARY OF SIMULATIONS (1ST 10 OF &NSAMPLES)";
  FORMAT M1_PV_9 - M1_PV_12 B0_2 ASE_1 ASE_3 6.1; ID SAMPLE ;
  VAR M1_PV_9 - M1_PV_12 B0_2 ASE_1 ASE_3 ; RUN ;
  PROC PRINT DATA=SUMRY(OBS=10) NOOBS;
  FORMAT B0_3 B1 M3_PV_9 - M3_PV_12 ASE_2 6.1 ; ID SAMPLE ;
  VAR  B0_3 B1 M3_PV_9 - M3_PV_12 ASE_2 ; RUN ;
  PROC PRINT DATA=SUMRY(OBS=10) NOOBS ;
  VAR S1-S3 V1-V3 F12 F13 F32 ;                 ID SAMPLE ;
  FORMAT S1-S3 V1-V3 F12 F13 F32 6.1 ;  RUN ;
  PROC PRINT DATA=SUMRY(OBS=10) NOOBS ;
  VAR P12 P13 P32
      PR12_05 PR12_01 PR13_05 PR13_01 PR32_05 PR32_01 ; ID SAMPLE ;
  FORMAT P12 P13 P32 6.3
      PR12_05 PR12_01 PR13_05 PR13_01 PR32_05 PR32_01 6.2 ; RUN ;
  PROC MEANS DATA = SUMRY MAXDEC=2 ;
  TITLE1 'DESCRIPTIVE STATS OF PARTIAL SAMPLING DISTRIBUTIONS';
  VAR    M1_PV_9 M1_PV_10 M1_PV_11 M1_PV_12 B0_2 B0_3 B1
         M3_PV_9 M3_PV_10 M3_PV_11 M3_PV_12 ASE_1-ASE_3
         S1-S3 V1-V3  F12 F13 F32
         PR12_05 PR12_01 PR13_05 PR13_01 PR32_05 PR32_01; RUN ;