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!'最小2乗法により回帰式を求める。
LET N =15
RANDOMIZE
DIM X(N),Y(N)
LET A=INT(RND*5)+1
LET B=INT(RND*3)+1
LET C=INT(RND*1000)+500
LET MODE=INT(RND*8)+1
FOR I =1 TO N
LET X(I)=I*2-1
SELECT CASE MODE
CASE 1
LET Y(I)=C/(A+B*X(I))
CASE 2
LET Y(I)=C/(A*EXP(B*X(I)))
CASE 3
LET Y(I)=C/(A*X(I)^B)
CASE 4
LET Y(I)=C/(B*LOG(X(I))+A)
CASE 5
LET Y(I)=C/(A*B^X(I))
CASE 6
LET Y(I)=C/(A+B*SQR(X(I)))
CASE 7
LET Y(I)=C/(A+B/X(I))
CASE 8
LET Y(I)=C/(A+B*X(I)^(1/3))
END SELECT
NEXT I
FOR I=1 TO N
PRINT "X=";X(I);"Y=";Y(I);"^Y=";
SELECT CASE MODE
CASE 1
PRINT FORECAST(X(I),N,Y,X)
CASE 2
PRINT FORECAST2(X(I),N,Y,X)
CASE 3
PRINT FORECAST3(X(I),N,Y,X)
CASE 4
PRINT FORECAST4(X(I),N,Y,X)
CASE 5
PRINT FORECAST5(X(I),N,Y,X)
CASE 6
PRINT FORECAST6(X(I),N,Y,X)
CASE 7
PRINT FORECAST7(X(I),N,Y,X)
CASE 8
PRINT FORECAST8(X(I),N,Y,X)
END SELECT
NEXT I
END
EXTERNAL FUNCTION FORECAST(X,N,YA(),XA())
!'Y=C/(A+B*X)
DIM XX(2,2),YY(2),WW(2)
FOR I=1 TO N
LET C=MAX(C,1/YA(I))
NEXT I
FOR I=1 TO N
LET XX(1,1)=XX(1,1)+1/C
LET XX(2,1)=XX(2,1)+XA(I)/C
LET XX(1,2)=XX(1,2)+XA(I)/C
LET XX(2,2)=XX(2,2)+XA(I)*XA(I)/C
LET YY(1)=YY(1)+1/YA(I)
LET YY(2)=YY(2)+1/YA(I)*XA(I)
NEXT I
CALL CRAMER2(XX,YY,WW)
LET A=WW(1)
LET B=WW(2)
LET FORECAST =C/(A+B*X)
END FUNCTION
EXTERNAL FUNCTION FORECAST2(X,N,YA(),XA())
!'Y=C/(A*EXP(B*X))
DIM XX(2,2),YY(2),WW(2)
LET C=-10000
FOR I=1 TO N
LET C=MAX(C,LOG(1/YA(I)))
NEXT I
FOR I=1 TO N
LET XX(1,1)=XX(1,1)+1
LET XX(2,1)=XX(2,1)+XA(I)
LET XX(1,2)=XX(1,2)+XA(I)
LET XX(2,2)=XX(2,2)+XA(I)*XA(I)
LET YY(1)=YY(1)+LOG(1/YA(I))
LET YY(2)=YY(2)+LOG(1/YA(I))*XA(I)
NEXT I
CALL CRAMER2(XX,YY,WW)
LET A=EXP(WW(1))*C
LET B=WW(2)
LET FORECAST2 =C/(A*EXP(B*X))
END FUNCTION
EXTERNAL FUNCTION FORECAST3(X,N,YA(),XA())
!'Y=C/(A*X^B)
DIM XX(2,2),YY(2),WW(2)
LET C=-10000
FOR I=1 TO N
LET C=MAX(C,LOG(1/YA(I)))
NEXT I
FOR I=1 TO N
LET XX(1,1)=XX(1,1)+1
LET XX(2,1)=XX(2,1)+LOG(XA(I))
LET XX(1,2)=XX(1,2)+LOG(XA(I))
LET XX(2,2)=XX(2,2)+LOG(XA(I))*LOG(XA(I))
LET YY(1)=YY(1)+LOG(1/YA(I))
LET YY(2)=YY(2)+LOG(1/YA(I))*LOG(XA(I))
NEXT I
CALL CRAMER2(XX,YY,WW)
LET A=EXP(WW(1))*C
LET B=WW(2)
LET FORECAST3 =C/(A*X^B)
END FUNCTION
EXTERNAL FUNCTION FORECAST4(X,N,YA(),XA())
!'Y=C/(B*LOG(X)+A)
DIM XX(2,2),YY(2),WW(2)
FOR I=1 TO N
LET C=MAX(C,1/YA(I))
NEXT I
FOR I=1 TO N
LET XX(1,1)=XX(1,1)+1/C
LET XX(2,1)=XX(2,1)+LOG(XA(I))/C
LET XX(1,2)=XX(1,2)+LOG(XA(I))/C
LET XX(2,2)=XX(2,2)+LOG(XA(I))*LOG(XA(I))/C
LET YY(1)=YY(1)+1/YA(I)
LET YY(2)=YY(2)+1/YA(I)*LOG(XA(I))
NEXT I
CALL CRAMER2(XX,YY,WW)
LET A=WW(1)
LET B=WW(2)
LET FORECAST4 =C/(B*LOG(X)+A)
END FUNCTION
EXTERNAL FUNCTION FORECAST5(X,N,YA(),XA())
!'Y=C/(A*B^X)
DIM XX(2,2),YY(2),WW(2)
LET C=-100000
FOR I=1 TO N
LET C=MAX(C,LOG(1/YA(I)))
NEXT I
FOR I=1 TO N
LET XX(1,1)=XX(1,1)+1
LET XX(2,1)=XX(2,1)+XA(I)
LET XX(1,2)=XX(1,2)+XA(I)
LET XX(2,2)=XX(2,2)+XA(I)*XA(I)
LET YY(1)=YY(1)+LOG(1/YA(I))
LET YY(2)=YY(2)+LOG(1/YA(I))*XA(I)
NEXT I
CALL CRAMER2(XX,YY,WW)
LET A=EXP(WW(1))*C
LET B=EXP(WW(2))
LET FORECAST5 =C/(A*B^X)
END FUNCTION
EXTERNAL FUNCTION FORECAST6(X,N,YA(),XA())
!'Y=C/(A+B*SQR(X))
DIM XX(2,2),YY(2),WW(2)
FOR I=1 TO N
LET C=MAX(C,1/YA(I))
NEXT I
FOR I=1 TO N
LET XX(1,1)=XX(1,1)+1/C
LET XX(2,1)=XX(2,1)+SQR(XA(I))/C
LET XX(1,2)=XX(1,2)+SQR(XA(I))/C
LET XX(2,2)=XX(2,2)+SQR(XA(I))*SQR(XA(I))/C
LET YY(1)=YY(1)+1/YA(I)
LET YY(2)=YY(2)+1/YA(I)*SQR(XA(I))
NEXT I
CALL CRAMER2(XX,YY,WW)
LET A=WW(1)
LET B=WW(2)
LET FORECAST6 =C/(A+B*SQR(X))
END FUNCTION
EXTERNAL FUNCTION FORECAST7(X,N,YA(),XA())
!'Y=C/(A+B*(1/X))
DIM XX(2,2),YY(2),WW(2)
FOR I=1 TO N
LET C=MAX(C,1/YA(I))
NEXT I
FOR I=1 TO N
LET XX(1,1)=XX(1,1)+1/C
LET XX(2,1)=XX(2,1)+1/XA(I)/C
LET XX(1,2)=XX(1,2)+1/XA(I)/C
LET XX(2,2)=XX(2,2)+1/XA(I)/XA(I)/C
LET YY(1)=YY(1)+1/YA(I)
LET YY(2)=YY(2)+1/YA(I)/XA(I)
NEXT I
CALL CRAMER2(XX,YY,WW)
LET A=WW(1)
LET B=WW(2)
LET FORECAST7 =C/(A+B/X)
END FUNCTION
EXTERNAL FUNCTION FORECAST8(X,N,YA(),XA())
!'Y=C/(A+B*X^(1/3))
DIM XX(2,2),YY(2),WW(2)
FOR I=1 TO N
LET C=MAX(C,1/YA(I))
NEXT I
FOR I=1 TO N
LET XX(1,1)=XX(1,1)+1/C
LET XX(2,1)=XX(2,1)+(XA(I)^(1/3))/C
LET XX(1,2)=XX(1,2)+(XA(I)^(1/3))/C
LET XX(2,2)=XX(2,2)+(XA(I)^(2/3))/C
LET YY(1)=YY(1)+1/YA(I)
LET YY(2)=YY(2)+1/YA(I)*XA(I)^(1/3)
NEXT I
CALL CRAMER2(XX,YY,WW)
LET A=WW(1)
LET B=WW(2)
LET FORECAST8 =C/(A+B*X^(1/3))
END FUNCTION
EXTERNAL SUB CRAMER2(X(,),Y(),W()) !'クラーメル法
LET D=X(1,1)*X(2,2)-X(2,1)*X(1,2)
LET XX=Y(1)*X(2,2)-Y(2)*X(1,2)
LET YY=Y(2)*X(1,1)-Y(1)*X(2,1)
LET W(1)=XX/D
LET W(2)=YY/D
END SUB
!'EXTERNAL SUB CRAMER3 (X(,), Y(), W())
!'LET D = X(1, 1) * X(2, 2) * X(3, 3) + X(2, 1) * X(3, 2) * X(1, 3) + X(3, 1) * X(1, 2) * X(2, 3) - X(3, 1) * X(2, 2) * X(1, 3) - X(2, 1) * X(1, 2) * X(3, 3) - X(1, 1) * X(3, 2) * X(2, 3)
!'LET XX = Y(1) * X(2, 2) * X(3, 3) + Y(2) * X(3, 2) * X(1, 3) + Y(3) * X(1, 2) * X(2, 3) - Y(3) * X(2, 2) * X(1, 3) - Y(2) * X(1, 2) * X(3, 3) - Y(1) * X(3, 2) * X(2, 3)
!'LET YY = X(1, 1) * Y(2) * X(3, 3) + X(2, 1) * Y(3) * X(1, 3) + X(3, 1) * Y(1) * X(2, 3) - X(3, 1) * Y(2) * X(1, 3) - X(2, 1) * Y(1) * X(3, 3) - X(1, 1) * Y(3) * X(2, 3)
!'LET ZZ = X(1, 1) * X(2, 2) * Y(3) + X(2, 1) * X(3, 2) * Y(1) + X(3, 1) * X(1, 2) * Y(2) - X(3, 1) * X(2, 2) * Y(1) - X(2, 1) * X(1, 2) * Y(3) - X(1, 1) * X(3, 2) * Y(2)
!'LET W(1) = XX / D
!'LET W(2) = YY / D
!'LET W(3) = ZZ / D
!'END SUB
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