uncertainty in linear fit

Hi all!

I want to ask about the uncertainty in the slope and in the constant term in a linear fit.

I found two function:

[p,S,mu] = polyfit(x,y,1); 
[ynew,delta]= polyval(p,x,S,mu);

and

cf = fit(x,y,'poly1'); 
cf_coeff = coeffvalues(cf);
cf_confint = confint(cf);
a = cf_coeff(1);
b = cf_coeff(2);
a_uncert = (cf_confint(2,1) - cf_confint(1,1))/2;
b_uncert = (cf_confint(2,2) - cf_confint(1,2))/2;

when i apply the two functions in my x,y data i find different coefficient. What is the different between the two functions and how can i apply them in x{a},y{a} data?

Thank you!

[Liviu Ivanescu]

polyval gives errors on y, not on slope or intercept.

Answer 1

[Jos (10584)]

Unfortunately, the first output of the function polyfit, being the coefficients of the fit changes, with the requested number of outputs. As an example:

x = 1:10 ;
y = 2*x + 3 ; 
p1 = polyfit(x,y,1)
[p2, S] = polyfit(x,y,1)
[p3, S, mu] = polyfit(x,y,1) % p3 is different!

This is only very cryptically mentioned in the documentation and is easily overlooked. I am not sure why this behaviour is implemented, but The Mathworks is likely to have its reasons ...

I suggest you to use the function fit to estimate the uncertainty in the parameters, as these are easy to retrieve. If you only need the coefficients, p = polyfit(x,y,n) will do, of course.

[Liviu Ivanescu]

[p3, S, mu] = polyfit(x,y,1)

uses a scaled version of x, see docs on polyfit for details ; that's why one gets different results.