分 60 70 WRITE(6,80) 80 FORMAT(IX.'n-G10.4G10.4.*X+ 100 ,G18.6/5XU G18.6 END (8分 COMMONAX/ACO.(50.10) 050 D010K=1,N 8 /(DBLE(N) D040I=1,M1 DO30 K=IN St-DsoRTSmV2 D0501白，M K-IN 50 ALIOQ=ALIO(D+(X(K.D-XV(D)*(X(K.MI)-XV(MI)) D060P060; ,M 60 X(K.I- (X(K.D-XV(S(D) I-IM DO70K-IN 70 A(IJ)=A(IJ)+X(K.I*X(K.J) DO 80 I M-I D08 S 11 ormal equation A(m,m+1y.2x,'m=,i2/1x,60(1H-)) D090=1,M 90 CALL G J=1.MI) WRITE(6,22) B006,33)(A,MI),e1.M0 U=0.D0 OMD-ACMI"SCMISO) 100 BOU-U-ACMIALIOXD)
6 50 FORMAT(3X,10G10.4) WRITE(6,60) (XV(I),I=1,M1) 60 FORMAT(/1X,'Xv',10G10.4) WRITE(6,70) (S(I),I=1,M1) 70 FORMAT(/1X,'Sv',10G10.4) WRITE(6,80) 80 FORMAT(/5X,'Regression equation is:',/1x,60(1H-)) WRITE(6,90) B0,(A(I,M1),I=1,M) 90 FORMAT(1X,'η=',G10.4,'+',G10.4,'*X1','+', & G10.4,'*X2','+',G10.4,'*X3') WRITE(6,100) QT,U,QE,SE,U/QT,R,F 100 FORMAT(/5X,'Qt=',G18.6,/5X,'U=',G18.6,/5X,'Qe=',G18.6,/5X, & 'Se=',G18.6,/5X,'N=',G18.6,/5X,'R=',G18.6,/5X,'F=', & G18.6) END SUBROUTINE MLR(M,N,XV,S,B0,QT,U,QE,SE,R,F) （8 分） DOUBLE PRECISION XV,S,A,X,B0,QT,U,QE,SE,R,F DIMENSION XV(M+1),S(M+1),ALI0(50) COMMON /AX/A(10,11),X(50,10) M1=M+1 DO 20 I=1,M1 XV(I)=0.D0 DO 10 K=1,N 10 XV(I)=XV(I)+X(K,I) 20 XV(I)=XV(I)/DBLE(N) DO 40 I=1,M1 S(I)=0 DO 30 K=1,N 30 S(I)=S(I)+(X(K,I)-XV(I))**2 40 S(I)=DSQRT(S(I)) DO 50 I=1,M ALI0(I)=0 DO 50 K=1,N 50 ALI0(I)=ALI0(I)+(X(K,I)-XV(I))*(X(K,M1)-XV(M1)) DO 60 I=1,M1 DO 60 K=1,N 60 X(K,I)=(X(K,I)-XV(I))/S(I) DO 70 I=1,M A(I,I)=1.0 DO 70 J=I+1,M1 A(I,J)=0 DO 70 K=1,N 70 A(I,J)=A(I,J)+X(K,I)*X(K,J) DO 80 I=1,M-1 DO 80 J=I+1,M 80 A(J,I)=A(I,J) WRITE(6,11) M 11 FORMAT(4X,'Normal equation A(m,m+1)',2x,'m=',i2/1x,60(1H-)) DO 90 I=1,M 90 WRITE(6,33) (A(I,J),J=1,M1) CALL GS(A,M,M1,1.D-06) WRITE(6,22) WRITE(6,33) (A(I,M1),I=1,M) B0=0.D0 U=0.D0 DO 100 I=1,M A(I,M1)=A(I,M1)*S(M1)/S(I) B0=B0+A(I,M1)*XV(I) 100 U=U+A(I,M1)*ALI0(I)
BO=XV(MIBO QT=S(MI)S(MI) SE=DSORT(QE/(N-M-D)) R=DSQRT(1.DO-QE/QT) FORMAT(/4X.'Roots of mormal equation''A(i.m+1).i=1.m'& 33 01oG24 RETURN END SUBROUTINE GS(A.N.M,EPS) (7分) EPS.A 0I=K IF(P.GE.ABS(A(LK))NGOTO 10 ABS(A(LK)) 10 CONTINUE O SOLUTION DO 20J=K.M A A(K.J)=TMP A(IJ)=A(IJA(I.K)*A(K.J) I=060k2N D060J+1，N 60 END 4.运行结果。(20分) Normal equation A(m,m+1)m=3 (5分) 1,000 .7608 8457E-01 -5228 1.000 .7747 Roots of mormal equationA(i,m+1),i=1,m -4482 .4943 .6921 INPUT DATA:Xnl.Xn2.....Xnm.Yn(m=1.3.n=1,6) XI X2 X3Y=n XI X2 X3 DIFF
7 B0=XV(M1)-B0 QT=S(M1)*S(M1) QE=QT-U SE=DSQRT(QE/(N-M-1)) R=DSQRT(1.D0-QE/QT) F=(N-M-1)*U/QE/M 22 FORMAT(/4X,'Roots of mormal equation','A(i,m+1),i=1,m' & /1x,60(1H-)) 33 FORMAT(1X,10G12.4) RETURN END SUBROUTINE GS(A,N,M,EPS) （7 分） DOUBLE PRECISION EPS,A DIMENSION A(10,11) DO 50 K=1,N P=0.0 DO 10 I=K,N IF(P.GE.ABS(A(I,K)))GOTO 10 P=ABS(A(I,K)) L=I 10 CONTINUE IF(P.LT.EPS)STOP'NO SOLUTION' IF(L.EQ.K)GOTO 30 DO 20 J=K,M TMP=A(L,J) A(L,J)=A(K,J) A(K,J)=TMP 20 CONTINUE 30 P=1.0/A(K,K) DO 40 J=K+1,M A(K,J)=A(K,J)*P DO 40 I=K+1,N A(I,J)=A(I,J)-A(I,K)*A(K,J) 40 CONTINUE 50 CONTINUE DO 60 K=2,N I=M-K DO 60 J=I+1,N A(I,M)=A(I,M)-A(I,J)*A(J,M) 60 CONTINUE RETURN END 4.运行结果。（20 分） Normal equation A(m,m+1) m= 3 （5 分） ------------------------------------------------------------ 1.000 .2623 -.7608 -.8451 .2623 1.000 -.5228 .1497E-01 -.7608 -.5228 1.000 .7747 Roots of mormal equationA(i,m+1),i=1,m ------------------------------------------------------------ -.4482 .4943 .6921 INPUT DATA:Xn1, Xn2,.... Xnm,Yn(m=1, 3,n=1, 6) X1 X2 X3 Y=η ------------------------------------------------------------------ X1 X2 X3 Y Ycalc DIFF