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!'最小2乗法により回帰式を求める。
LET N = 15 !'データ数
RANDOMIZE
DIM X(N), Y(N)
LET A = RND !'乱数で係数を決める
LET B = RND
LET MODE=INT(RND*8)+1
FOR I =1 TO N
LET X(I)=I
SELECT CASE MODE !'仮データ作成
CASE 1
LET Y(I)=A+B*X(I)
CASE 2
LET Y(I)=EXP(A*X(I))*B
CASE 3
LET Y(I)=A*X(I)^B
CASE 4
LET Y(I)=A*LOG(X(I))+B
CASE 5
LET Y(I)=A*B^X(I)
CASE 6
LET Y(I)=A*SQR(X(I))+B
CASE 7
LET Y(I)=A/X(I)+B
CASE 8
LET Y(I)=A*X(I)^(1/3)+B
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
!'PRINT "R2=";R2(N,Y,X)
END
EXTERNAL FUNCTION R2(N,YA(),XA()) !'決定係数(寄与率) 0<=r^2<=1
LET YN=MEAN(N,YA)
FOR I=1 TO N
LET YY=FORECAST(XA(I),N,YA,XA)
!' LET YY=FORECAST2(XA(I),N,YA,XA)
!' LET YY=FORECAST3(XA(I),N,YA,XA)
!' LET YY=FORECAST4(XA(I),N,YA,XA)
!' LET YY=FORECAST5(XA(I),N,YA,XA)
!' LET YY=FORECAST6(XA(I),N,YA,XA)
!' LET YY=FORECAST7(XA(I),N,YA,XA)
!' LET YY=FORECAST8(XA(I),N,YA,XA)
LET SY=SY+(YA(I)-YN)^2
LET SE=SE+(YA(I)-YY)^2
NEXT I
LET R2=1-SE/SY
END FUNCTION
EXTERNAL FUNCTION MEAN(N,X()) !'平均
FOR I=1 TO N
LET S=S+X(I)
NEXT I
LET MEAN=S/N
END FUNCTION
EXTERNAL FUNCTION SLOPEA(N,YA(),XA())
LET XN=MEAN(N,XA)
LET YN=MEAN(N,YA)
FOR I=1 TO N
LET X=X+(XA(I)-XN)^2
LET XY=XY+(XA(I)-XN)*(YA(I)-YN)
NEXT I
LET SLOPEA=XY/X
END FUNCTION
EXTERNAL FUNCTION INTERCEPTA(N, YA(), XA())
LET B = SLOPEA(N, YA, XA)
FOR I = 1 TO N
LET A = A + YA(I) - B * XA(I)
NEXT I
LET INTERCEPTA = A / N
END FUNCTION
EXTERNAL FUNCTION FORECASTA(X, N, YA(), XA())
!'Y=B+A*X
LET A = SLOPEA(N, YA, XA)
LET B = INTERCEPTA(N, YA, XA)
LET FORECASTA = B + A * X
END FUNCTION
EXTERNAL FUNCTION SLOPE(N, YA(), XA())
FOR I = 1 TO N
LET XY = XY + XA(I) * YA(I)
LET X = X + XA(I)
LET Y = Y + YA(I)
LET XX = XX + XA(I) * XA(I)
NEXT I
LET SLOPE = (N * XY - X * Y) / (N * XX - X * X)
END FUNCTION
EXTERNAL FUNCTION INTERCEPT(N, YA(), XA())
FOR I = 1 TO N
LET XY = XY + XA(I) * YA(I)
LET X = X + XA(I)
LET Y = Y + YA(I)
LET XX = XX + XA(I) * XA(I)
NEXT I
LET INTERCEPT = (Y * XX - XY * X) / (N * XX - X * X)
END FUNCTION
EXTERNAL FUNCTION FORECAST(X, N, YA(), XA())
!'Y=B+A*X
LET A = SLOPE(N, YA, XA)
LET B = INTERCEPT(N, YA, XA)
LET FORECAST = B + A * X
END FUNCTION
EXTERNAL FUNCTION SLOPE2(N, YA(), XA())
FOR I = 1 TO N
LET XY = XY + XA(I) * LOG(YA(I))
LET X = X + XA(I)
LET Y = Y + LOG(YA(I))
LET XX = XX + XA(I) * XA(I)
NEXT I
LET SLOPE2 = (N * XY - X * Y) / (N * XX - X * X)
END FUNCTION
EXTERNAL FUNCTION INTERCEPT2(N, YA(), XA())
FOR I = 1 TO N
LET XY = XY + XA(I) * LOG(YA(I))
LET X = X + XA(I)
LET Y = Y + LOG(YA(I))
LET XX = XX + XA(I) * XA(I)
NEXT I
LET INTERCEPT2 = EXP((Y * XX - XY * X) / (N * XX - X * X))
END FUNCTION
EXTERNAL FUNCTION FORECAST2(X, N, YA(), XA())
!'y=b*EXP(a*x)
!'LOG(y)=LOG(b)+a*x
!'Y=LOG(y) B=LOG(b) A=a X=x
!'Y=B+A*X
!'b=EXP(B)
LET A = SLOPE2(N, YA, XA)
LET B = INTERCEPT2(N, YA, XA)
LET FORECAST2 = B * EXP(A * X)
END FUNCTION
EXTERNAL FUNCTION SLOPE3(N, YA(), XA())
FOR I = 1 TO N
LET XY = XY + LOG(XA(I)) * LOG(YA(I))
LET X = X + LOG(XA(I))
LET Y = Y + LOG(YA(I))
LET XX = XX + LOG(XA(I)) * LOG(XA(I))
NEXT I
LET SLOPE3 = (N * XY - X * Y) / (N * XX - X * X)
END FUNCTION
EXTERNAL FUNCTION INTERCEPT3(N, YA(), XA())
FOR I = 1 TO N
LET XY = XY + LOG(XA(I)) * LOG(YA(I))
LET X = X + LOG(XA(I))
LET Y = Y + LOG(YA(I))
LET XX = XX + LOG(XA(I)) * LOG(XA(I))
NEXT I
LET INTERCEPT3 = EXP((Y * XX - XY * X) / (N * XX - X * X))
END FUNCTION
EXTERNAL FUNCTION FORECAST3(X, N, YA(), XA())
!'y=a*x^b
!'LOG(y)=LOG(a)+b*LOG(x)
!'Y=LOG(y) A=b B=LOG(a) X=LOG(x)
!'Y=B+A*X
!'a=EXP(B)
LET B = SLOPE3(N, YA, XA)
LET A = INTERCEPT3(N, YA, XA)
LET FORECAST3 = A * X ^ B
END FUNCTION
EXTERNAL FUNCTION SLOPE4(N, YA(), XA())
FOR I = 1 TO N
LET XY = XY + LOG(XA(I)) * YA(I)
LET X = X + LOG(XA(I))
LET Y = Y + YA(I)
LET XX = XX + LOG(XA(I)) * LOG(XA(I))
NEXT I
LET SLOPE4 = (N * XY - X * Y) / (N * XX - X * X)
END FUNCTION
EXTERNAL FUNCTION INTERCEPT4(N, YA(), XA())
FOR I = 1 TO N
LET XY = XY + LOG(XA(I)) * YA(I)
LET X = X + LOG(XA(I))
LET Y = Y + YA(I)
LET XX = XX + LOG(XA(I)) * LOG(XA(I))
NEXT I
LET INTERCEPT4 = (Y * XX - XY * X) / (N * XX - X * X)
END FUNCTION
EXTERNAL FUNCTION FORECAST4(X, N, YA(), XA())
!'y=b+a*LOG(x)
!'Y=y A=a X=LOG(x) B=b
!'Y=B+A*X
LET A = SLOPE4(N, YA, XA)
LET B = INTERCEPT4(N, YA, XA)
LET FORECAST4 = A * LOG(X) + B
END FUNCTION
EXTERNAL FUNCTION SLOPE5(N, YA(), XA())
FOR I = 1 TO N
LET XY = XY + XA(I) * LOG(YA(I))
LET X = X + XA(I)
LET Y = Y + LOG(YA(I))
LET XX = XX + XA(I) * XA(I)
NEXT I
LET SLOPE5 = EXP((N * XY - X * Y) / (N * XX - X * X))
END FUNCTION
EXTERNAL FUNCTION INTERCEPT5(N, YA(), XA())
FOR I = 1 TO N
LET XY = XY + XA(I) * LOG(YA(I))
LET X = X + XA(I)
LET Y = Y + LOG(YA(I))
LET XX = XX + XA(I) * XA(I)
NEXT I
LET INTERCEPT5 = EXP((Y * XX - XY * X) / (N * XX - X * X))
END FUNCTION
EXTERNAL FUNCTION FORECAST5(X, N, YA(), XA())
!'y=a*b^x
!'LOG(y)=LOG(a)+LOG(b)*x
!'Y=LOG(y) B=LOG(a) X=x A=LOG(b)
!'Y=B+A*X
!'a=EXP(B) b=EXP(A)
LET B = SLOPE5(N, YA, XA)
LET A = INTERCEPT5(N, YA, XA)
LET FORECAST5 = A * B ^ X
END FUNCTION
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