最小自乗法には fit を用いる。 最初に乗るべき関数を定義したあと、パラメータを計算させる。
> plot "planet081104_dat" > f(x) = a * sin(x) + b * cos(x) + c
使ったデータはこれ
> fit f(x) "planet081104_dat.dat" via a, b, c
Iteration 0
WSSR : 1.09142e+19 delta(WSSR)/WSSR : 0
delta(WSSR) : 0 limit for stopping : 1e-05
lambda : 0.816497
initial set of free parameter values
a = 1.66317e+09
b = -2.15942e+08
c = 5.04586e+08
**/
Iteration 1
WSSR : 1.09142e+19 delta(WSSR)/WSSR : -3.7529e-16
delta(WSSR) : -4096 limit for stopping : 1e-05
lambda : 8.16497
resultant parameter values
a = 1.66317e+09
b = -2.15942e+08
c = 5.04586e+08
After 1 iterations the fit converged.
final sum of squares of residuals : 1.09142e+19
rel. change during last iteration : -3.7529e-16
degrees of freedom (ndf) : 6
rms of residuals (stdfit) = sqrt(WSSR/ndf) : 1.34872e+09
variance of residuals (reduced chisquare) = WSSR/ndf : 1.81904e+18
Final set of parameters Asymptotic Standard Error
======================= ==========================
a = 1.66317e+09 +/- 6.271e+08 (37.71%)
b = -2.15942e+08 +/- 7.384e+08 (341.9%)
c = 5.04586e+08 +/- 5.132e+08 (101.7%)
correlation matrix of the fit parameters:
a b c
a 1.000
b -0.070 1.000
c 0.114 -0.475 1.000
最小自乗法のパラメータを計算したあとに
> replot f(x)