# Polyfit and parameter uncertainty

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Niles Martinsen on 22 Jun 2012
Commented: Kamal Gurnani on 28 Feb 2019
Hi
I have some data (x, y), where y is proportional to x. I want to find the relationship, so I fit a function of the form f(x) = a*x+b to the data. This is how I do it:
p_RvsT = polyfit(r_vs_t(:, 1), r_vs_t(:, 2), 1);
Now this gives me a good estimate of a and b. What I want now is to find the uncertainty (= standard deviation) on the estimated values of a and b. I have found an older thread ( http://www.mathworks.com/matlabcentral/newsreader/view_thread/59468), which uses this technique:
x=1:100:10000;
y=x+.1*x.*(rand(size(x))-.5);
[p,s]=polyfit(x,y,1);
[yh,d]=polyval(p,x,s);
% show results
line(x,y);
line(x,[yh;yh-d;yh+d],'color',[1 0 0]);
My question is if this is the correct way to do so?
Best,
Niles.

Walter Roberson on 22 Jun 2012
Yes.
Niles Martinsen on 22 Jun 2012
Thanks for the quick help.
Kamal Gurnani on 28 Feb 2019
But the d-values are the prediction intervals for y, I still can not see the uncertainities in the coefficients.