Polyfit and parameter uncertainty

Question

Niles Martinsen 2012-6-22

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/41845-polyfit-and-parameter-uncertainty

评论： Kamal Gurnani 2019-2-28

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]);