求高手知道指数函数拟合
x=5:5:70;y=;
y=c*exp(-c*x);
C是系数，想通过上面数据求出c。
General model Exp1:
f(x) = a*exp(b*x)
Coefficients (with 95% confidence bounds):
a = 0.7751 (0.7252, 0.825)
b = -0.1184 (-0.1262, -0.1105)
Goodness of fit:
SSE: 0.000652
R-square: 0.9966
Adjusted R-square: 0.9964
RMSE: 0.007371
General model:
f(x) = c*exp(-c*x)
Coefficients (with 95% confidence bounds):
c = 0.1458 (-0.8828, 1.174)
Goodness of fit:
SSE: 0.1899
R-square: 0.02284
Adjusted R-square: 0.02284
RMSE: 0.1209
LINGO也能实现：SETS:
VAR/ 1..14/: X, Y;
ENDSETS
DATA:
Y= 0.4293 0.2417 0.1240 0.0604 0.0493 0.0270 0.0223 0.0095 0.0079 0.0048 0.0064 0.0032 0.0016 0.0127;
ENDDATA
CALC:
X( 1) = 5;
@FOR( VAR( I)| I #GE# 2: X( I) = X( I - 1) + 5);
ENDCALC
MIN=RS;
RS = @SUM( VAR( I): (C * @EXP( -C * X( I)) - Y( I))^ 2);
CALC:
@SET('GLOBAL', 1);
ENDCALC结果：Global optimal solution found.
Objective value: 0.1899075
Objective bound: 0.1899066
Infeasibilities: 0.000000
Extended solver steps: 103
Total solver iterations: 18999
Variable Value Reduced Cost
RS 0.1899075 0.000000
C 0.1458114 0.000000
X( 1) 5.000000 0.000000
X( 2) 10.00000 0.000000
X( 3) 15.00000 0.000000
X( 4) 20.00000 0.000000
X( 5) 25.00000 0.000000
X( 6) 30.00000 0.000000
X( 7) 35.00000 0.000000
X( 8) 40.00000 0.000000
X( 9) 45.00000 0.000000
X( 10) 50.00000 0.000000
X( 11) 55.00000 0.000000
X( 12) 60.00000 0.000000
X( 13) 65.00000 0.000000
X( 14) 70.00000 0.000000
Y( 1) 0.4293000 0.000000
Y( 2) 0.2417000 0.000000
Y( 3) 0.1240000 0.000000
Y( 4) 0.6040000E-01 0.000000
Y( 5) 0.4930000E-01 0.000000
Y( 6) 0.2700000E-01 0.000000
Y( 7) 0.2230000E-01 0.000000
Y( 8) 0.9500000E-02 0.000000
Y( 9) 0.7900000E-02 0.000000
Y( 10) 0.4800000E-02 0.000000
Y( 11) 0.6400000E-02 0.000000
Y( 12) 0.3200000E-02 0.000000
Y( 13) 0.1600000E-02 0.000000
Y( 14) 0.1270000E-01 0.000000
Row Slack or Surplus Dual Price
1 0.1899075 -1.000000
2 0.000000 -1.000000
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