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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