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!'最小2乗法により回帰式を求める(ロジスティック回帰式)
!'y=1/(1+EXP(-(a+bx))) 0<y<1
!'1/y=1+EXP(-(a+bx))
!'1/(1/y-1)=EXP(a+bx)
!'LOG(y/(1-y))=a+bx
!'Y=LOG(y/(1-y)) X=x A=a B=b
!' A + X*B + Y*C + Z*D + W*E = LOG(F(X,Y,Z,W)/(1-F(X,Y,Z,W)))
!'Σ1*1 ΣX*1 ΣY*1 ΣZ*1 ΣW*1 ΣLOG(F(X,Y,Z,W)/(1-F(X,Y,Z,W)))*1
!'Σ1*X ΣX*X ΣY*X ΣZ*X ΣW*X ΣLOG(F(X,Y,Z,W)/(1-F(X,Y,Z,W)))*X
!'Σ1*Y ΣX*Y ΣY*Y ΣZ*Y ΣW*Y ΣLOG(F(X,Y,Z,W)/(1-F(X,Y,Z,W)))*Y
!'Σ1*Z ΣX*Z ΣY*Z ΣZ*Z ΣW*Z ΣLOG(F(X,Y,Z,W)/(1-F(X,Y,Z,W)))*Z
!'Σ1*W ΣX*W ΣY*W ΣZ*W ΣW*W ΣLOG(F(X,Y,Z,W)/(1-F(X,Y,Z,W)))*W
LET N = 10
RANDOMIZE
DIM X(N),Y(N),Z(N),F(N)
LET A=RND
LET B=RND
LET C=RND
LET D=RND
LET M=INT(RND*3)+1
FOR I = 1 TO N
LET X(I) = RND
IF M>1 THEN LET Y(I) = RND
IF M>2 THEN LET Z(I) = RND
LET F(I) = 1/(1+EXP(-(A+B*X(I)+C*Y(I)+D*Z(I))))
NEXT I
SELECT CASE M
CASE 1
FOR I=1 TO N
PRINT "X=";X(I);"F(X)=";F(I);"^F(X)=";FORECAST(N,X,F,X(I))
NEXT I
CASE 2
FOR I=1 TO N
PRINT "X=";X(I);"Y=";Y(I);"F(X,Y)=";F(I);"^F(X,Y)=";FORECAST2(N,X,Y,F,X(I),Y(I))
NEXT I
CASE 3
FOR I=1 TO N
PRINT "X=";X(I);"Y=";Y(I);"Z=";Z(I);"F(X,Y,Z)=";F(I);"^F(X,Y,Z)=";FORECAST3(N,X,Y,Z,F,X(I),Y(I),Z(I))
NEXT I
END SELECT
END
EXTERNAL FUNCTION FORECAST(N,X(),F(),XA)
!'F(X)=1/(1+EXP(-(A+B*X)))
DIM XX(2,2),YY(2),WW(2)
FOR I=1 TO N
LET XX(1,1)=XX(1,1)+1
LET XX(2,1)=XX(2,1)+X(I)
LET XX(1,2)=XX(1,2)+X(I)
LET XX(2,2)=XX(2,2)+X(I)*X(I)
LET YY(1)=YY(1)+LOG(F(I)/(1-F(I)))
LET YY(2)=YY(2)+LOG(F(I)/(1-F(I)))*X(I)
NEXT I
CALL CRAMER(2,XX,YY,WW)
LET AA=WW(1)
LET BB=WW(2)
LET FORECAST = 1/(1+EXP(-(AA+BB*XA)))
END FUNCTION
EXTERNAL FUNCTION FORECAST2(N,X(),Y(),F(),XA,YA)
!'F(X,Y)=1/(1+EXP(-(A+B*X+C*Y)))
DIM XX(3,3),YY(3),WW(3)
FOR I=1 TO N
LET XX(1,1)=XX(1,1)+1
LET XX(2,1)=XX(2,1)+X(I)
LET XX(3,1)=XX(3,1)+Y(I)
LET XX(1,2)=XX(1,2)+X(I)
LET XX(2,2)=XX(2,2)+X(I)*X(I)
LET XX(3,2)=XX(3,2)+X(I)*Y(I)
LET XX(1,3)=XX(1,3)+Y(I)
LET XX(2,3)=XX(2,3)+Y(I)*X(I)
LET XX(3,3)=XX(3,3)+Y(I)*Y(I)
LET YY(1)=YY(1)+LOG(F(I)/(1-F(I)))
LET YY(2)=YY(2)+LOG(F(I)/(1-F(I)))*X(I)
LET YY(3)=YY(3)+LOG(F(I)/(1-F(I)))*Y(I)
NEXT I
CALL CRAMER(3,XX,YY,WW)
LET AA=WW(1)
LET BB=WW(2)
LET CC=WW(3)
LET FORECAST2 = 1/(1+EXP(-(AA+BB*XA+CC*YA)))
END FUNCTION
EXTERNAL FUNCTION FORECAST3(N,X(),Y(),Z(),F(),XA,YA,ZA)
!'F(X,Y,Z)=1/(1+EXP(-(A+B*X+C*Y+D*Z)))
DIM XX(4,4),YY(4),WW(4)
FOR I=1 TO N
LET XX(1,1)=XX(1,1)+1
LET XX(2,1)=XX(2,1)+X(I)
LET XX(3,1)=XX(3,1)+Y(I)
LET XX(4,1)=XX(4,1)+Z(I)
LET XX(1,2)=XX(1,2)+X(I)
LET XX(2,2)=XX(2,2)+X(I)*X(I)
LET XX(3,2)=XX(3,2)+X(I)*Y(I)
LET XX(4,2)=XX(4,2)+X(I)*Z(I)
LET XX(1,3)=XX(1,3)+Y(I)
LET XX(2,3)=XX(2,3)+Y(I)*X(I)
LET XX(3,3)=XX(3,3)+Y(I)*Y(I)
LET XX(4,3)=XX(4,3)+Y(I)*Z(I)
LET XX(1,4)=XX(1,4)+Z(I)
LET XX(2,4)=XX(2,4)+Z(I)*X(I)
LET XX(3,4)=XX(3,4)+Z(I)*Y(I)
LET XX(4,4)=XX(4,4)+Z(I)*Z(I)
LET YY(1)=YY(1)+LOG(F(I)/(1-F(I)))
LET YY(2)=YY(2)+LOG(F(I)/(1-F(I)))*X(I)
LET YY(3)=YY(3)+LOG(F(I)/(1-F(I)))*Y(I)
LET YY(4)=YY(4)+LOG(F(I)/(1-F(I)))*Z(I)
NEXT I
CALL CRAMER(4,XX,YY,WW)
LET AA=WW(1)
LET BB=WW(2)
LET CC=WW(3)
LET DD=WW(4)
LET FORECAST3 = 1/(1+EXP(-(AA+BB*XA+CC*YA+DD*ZA)))
END FUNCTION
EXTERNAL SUB CRAMER (N, X(,), Y(), D()) !'クラーメル法
DIM A(N, N)
FOR I=1 TO N
FOR J=1 TO N
LET A(I,J)=X(I,J)
NEXT J
NEXT I
LET DD = DET(A)
IF DD = 0 THEN STOP !'ERROR
FOR K = 1 TO N
FOR I = 1 TO N
FOR J = 1 TO N
IF J = K THEN LET A(I, J) = Y(I) ELSE LET A(I, J) = X(I, J)
NEXT J
NEXT I
LET D(K) = DET(A) / DD
NEXT K
END SUB
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