C MULT 10
C ..................................................................MULT 20
C MULT 30
C SUBROUTINE MULTR MULT 40
C MULT 50
C PURPOSE MULT 60
C PERFORM A MULTIPLE LINEAR REGRESSION ANALYSIS FOR A MULT 70
C DEPENDENT VARIABLE AND A SET OF INDEPENDENT VARIABLES. THISMULT 80
C SUBROUTINE IS NORMALLY USED IN THE PERFORMANCE OF MULTIPLE MULT 90
C AND POLYNOMIAL REGRESSION ANALYSES. MULT 100
C MULT 110
C USAGE MULT 120
C CALL MULTR (N,K,XBAR,STD,D,RX,RY,ISAVE,B,SB,T,ANS) MULT 130
C MULT 140
C DESCRIPTION OF PARAMETERS MULT 150
C N - NUMBER OF OBSERVATIONS. MULT 160
C K - NUMBER OF INDEPENDENT VARIABLES IN THIS REGRESSION. MULT 170
C XBAR - INPUT VECTOR OF LENGTH M CONTAINING MEANS OF ALL MULT 180
C VARIABLES. M IS NUMBER OF VARIABLES IN OBSERVATIONS.MULT 190
C STD - INPUT VECTOR OF LENGTH M CONTAINING STANDARD DEVI- MULT 200
C ATIONS OF ALL VARIABLES. MULT 210
C D - INPUT VECTOR OF LENGTH M CONTAINING THE DIAGONAL OF MULT 220
C THE MATRIX OF SUMS OF CROSS-PRODUCTS OF DEVIATIONS MULT 230
C FROM MEANS FOR ALL VARIABLES. MULT 240
C RX - INPUT MATRIX (K X K) CONTAINING THE INVERSE OF MULT 250
C INTERCORRELATIONS AMONG INDEPENDENT VARIABLES. MULT 260
C RY - INPUT VECTOR OF LENGTH K CONTAINING INTERCORRELA- MULT 270
C TIONS OF INDEPENDENT VARIABLES WITH DEPENDENT MULT 280
C VARIABLE. MULT 290
C ISAVE - INPUT VECTOR OF LENGTH K+1 CONTAINING SUBSCRIPTS OF MULT 300
C INDEPENDENT VARIABLES IN ASCENDING ORDER. THE MULT 310
C SUBSCRIPT OF THE DEPENDENT VARIABLE IS STORED IN MULT 320
C THE LAST, K+1, POSITION. MULT 330
C B - OUTPUT VECTOR OF LENGTH K CONTAINING REGRESSION MULT 340
C COEFFICIENTS. MULT 350
C SB - OUTPUT VECTOR OF LENGTH K CONTAINING STANDARD MULT 360
C DEVIATIONS OF REGRESSION COEFFICIENTS. MULT 370
C T - OUTPUT VECTOR OF LENGTH K CONTAINING T-VALUES. MULT 380
C ANS - OUTPUT VECTOR OF LENGTH 10 CONTAINING THE FOLLOWING MULT 390
C INFORMATION.. MULT 400
C ANS(1) INTERCEPT MULT 410
C ANS(2) MULTIPLE CORRELATION COEFFICIENT MULT 420
C ANS(3) STANDARD ERROR OF ESTIMATE MULT 430
C ANS(4) SUM OF SQUARES ATTRIBUTABLE TO REGRES- MULT 440
C SION (SSAR) MULT 450
C ANS(5) DEGREES OF FREEDOM ASSOCIATED WITH SSAR MULT 460
C ANS(6) MEAN SQUARE OF SSAR MULT 470
C ANS(7) SUM OF SQUARES OF DEVIATIONS FROM REGRES- MULT 480
C SION (SSDR) MULT 490
C ANS(8) DEGREES OF FREEDOM ASSOCIATED WITH SSDR MULT 500
C ANS(9) MEAN SQUARE OF SSDR MULT 510
C ANS(10) F-VALUE MULT 520
C MULT 530
C REMARKS MULT 540
C N MUST BE GREATER THAN K+1. MULT 550
C MULT 560
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED MULT 570
C NONE MULT 580
C MULT 590
C METHOD MULT 600
C THE GAUSS-JORDAN METHOD IS USED IN THE SOLUTION OF THE MULT 610
C NORMAL EQUATIONS. REFER TO W. W. COOLEY AND P. R. LOHNES, MULT 620
C 'MULTIVARIATE PROCEDURES FOR THE BEHAVIORAL SCIENCES', MULT 630
C JOHN WILEY AND SONS, 1962, CHAPTER 3, AND B. OSTLE, MULT 640
C 'STATISTICS IN RESEARCH', THE IOWA STATE COLLEGE PRESS, MULT 650
C 1954, CHAPTER 8. MULT 660
C MULT 670
C ..................................................................MULT 680
C MULT 690
SUBROUTINE MULTR (N,K,XBAR,STD,D,RX,RY,ISAVE,B,SB,T,ANS) MULT 700
DIMENSION XBAR(1),STD(1),D(1),RX(1),RY(1),ISAVE(1),B(1),SB(1), MULT 710
1 T(1),ANS(1) MULT 720
C MULT 730
C ...............................................................MULT 740
C MULT 750
C IF A DOUBLE PRECISION VERSION OF THIS ROUTINE IS DESIRED, THE MULT 760
C C IN COLUMN 1 SHOULD BE REMOVED FROM THE DOUBLE PRECISION MULT 770
C STATEMENT WHICH FOLLOWS. MULT 780
C MULT 790
C DOUBLE PRECISION XBAR,STD,D,RX,RY,B,SB,T,ANS,RM,BO,SSAR,SSDR,SY, MULT 800
C 1 FN,FK,SSARM,SSDRM,F MULT 810
C MULT 820
C THE C MUST ALSO BE REMOVED FROM DOUBLE PRECISION STATEMENTS MULT 830
C APPEARING IN OTHER ROUTINES USED IN CONJUNCTION WITH THIS MULT 840
C ROUTINE. MULT 850
C MULT 860
C THE DOUBLE PRECISION VERSION OF THIS SUBROUTINE MUST ALSO MULT 870
C CONTAIN DOUBLE PRECISION FORTRAN FUNCTIONS. SQRT AND ABS IN MULT 880
C STATEMENTS 122, 125, AND 135 MUST BE CHANGED TO DSQRT AND DABS.MULT 890
C MULT 900
C ...............................................................MULT 910
C MULT 920
MM=K+1 MULT 930
C MULT 940
C BETA WEIGHTS MULT 950
C MULT 960
DO 100 J=1,K MULT 970
100 B(J)=0.0 MULT 980
DO 110 J=1,K MULT 990
L1=K*(J-1) MULT1000
DO 110 I=1,K MULT1010
L=L1+I MULT1020
110 B(J)=B(J)+RY(I)*RX(L) MULT1030
RM=0.0 MULT1040
BO=0.0 MULT1050
L1=ISAVE(MM) MULT1060
C MULT1070
C COEFFICIENT OF DETERMINATION MULT1080
C MULT1090
DO 120 I=1,K MULT1100
RM=RM+B(I)*RY(I) MULT1110
C MULT1120
C REGRESSION COEFFICIENTS MULT1130
C MULT1140
L=ISAVE(I) MULT1150
B(I)=B(I)*(STD(L1)/STD(L)) MULT1160
C MULT1170
C INTERCEPT MULT1180
C MULT1190
120 BO=BO+B(I)*XBAR(L) MULT1200
BO=XBAR(L1)-BO MULT1210
C MULT1220
C SUM OF SQUARES ATTRIBUTABLE TO REGRESSION MULT1230
C MULT1240
SSAR=RM*D(L1) MULT1250
C MULT1260
C MULTIPLE CORRELATION COEFFICIENT MULT1270
C MULT1280
122 RM= SQRT( ABS(RM)) MULT1290
C MULT1300
C SUM OF SQUARES OF DEVIATIONS FROM REGRESSION MULT1310
C MULT1320
SSDR=D(L1)-SSAR MULT1330
C MULT1340
C VARIANCE OF ESTIMATE MULT1350
C MULT1360
FN=N-K-1 MULT1370
SY=SSDR/FN MULT1380
C MULT1390
C STANDARD DEVIATIONS OF REGRESSION COEFFICIENTS MULT1400
C MULT1410
DO 130 J=1,K MULT1420
L1=K*(J-1)+J MULT1430
L=ISAVE(J) MULT1440
125 SB(J)= SQRT( ABS((RX(L1)/D(L))*SY)) MULT1450
C MULT1460
C COMPUTED T-VALUES MULT1470
C MULT1480
130 T(J)=B(J)/SB(J) MULT1490
C MULT1500
C STANDARD ERROR OF ESTIMATE MULT1510
C MULT1520
135 SY= SQRT( ABS(SY)) MULT1530
C MULT1540
C F VALUE MULT1550
C MULT1560
FK=K MULT1570
SSARM=SSAR/FK MULT1580
SSDRM=SSDR/FN MULT1590
F=SSARM/SSDRM MULT1600
C MULT1610
ANS(1)=BO MULT1620
ANS(2)=RM MULT1630
ANS(3)=SY MULT1640
ANS(4)=SSAR MULT1650
ANS(5)=FK MULT1660
ANS(6)=SSARM MULT1670
ANS(7)=SSDR MULT1680
ANS(8)=FN MULT1690
ANS(9)=SSDRM MULT1700
ANS(10)=F MULT1710
RETURN MULT1720
END MULT1730