[Scilab-users] evaluate error on each parameter calculated with leastsq

[Serge Steer]

Le 19/02/2014 14:31, Yohann a écrit :
> Hi Antoine,
> thank you for your answer but
> what I need is a confidence interval on each parameter !
The confidence interval on the computed parameters depends on the 
confidence interval  on your x and y data.

In your case where you are looking for polynomial fitting then 
perturbations on y  produces perturbation on the computed parameters  
roughly proportionnal to the conditionning of the matrix A=[x*x x ones(x)]

if c is the mean square solution of the probleme for  y and c1 is the 
mean square solution of the problem of y1 then
norm(c-c1)/norm(c)<=cond(A)*norm(y-y1)/norm(y)

x = [ 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6]';
y = [5.02  6.08  3.33 -0.93   -0.22  7.83  16.52 15.55  2.67 -11.42 -11.78 5.09 25.25]';

A=[x.^2 x ones(x)];

y1=y;y1=y1.*(1+0.000001*rand(y1));ey=norm(y-y1)/norm(y)
c1=A\y1;ec=norm(c-c1)/norm(c)

ec<=cond(A)*ey

the dependance with respect to perturbation on x is more difficult.
> Cheers
> Yohann
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