How to get the coefficient uncertainty by polyfit?

I used the Matlab polynomial fit. I would then like to have the fit parameters with their uncertainty e.g. have a1 = 1,345 +/- 0.023 output.

fp are the fit parameters. There is a triangular matrix in error, which is output as an R variable. I know that this is somehow related to the Vandermonde matrix. But how do I get the uncertainties of the individual fit parameters?

I used these values ​​for testing in a .txt-Datei

DickeAFM(nm) KontrastRed

1.0000 0.5510

6.2105 2.1668

11.4211 3.6191

16.6316 3.8623

21.8421 2.5386

27.0526 1.3215

32.2632 0.0862

37.4737 -0.1983

42.6842 0.7642

47.8947 2.7360

53.1053 4.9756

58.3158 6.5082

63.5263 7.7232

68.7368 7.4745

73.9474 6.0571

79.1579 4.5283

84.3684 3.6237

89.5789 3.7593

94.7895 5.2323

100.0000 7.2310

delimiter = '\t'; 
startRow = 2; 
formatSpec = '%f%f%[^\n\r]';

[file,path] = uigetfile;
filename = fullfile(path, file);

fileID = fopen(filename,'r');
dataArray = textscan(fileID, formatSpec, 'Delimiter', delimiter, 'TextType', 'string', 'HeaderLines' ,startRow-1, 'ReturnOnError', false, 'EndOfLine', '\r\n');
fclose(fileID);
d=cell2mat(dataArray(1));
I=cell2mat(dataArray(2));


n=9;
[fP,Error]=polyfit(d,I,n);

Answer 1

[darova]

Try fit

x1 = linspace(x(1),x(end),100);
F=fit(x,y,'poly9')
plot(x,y)
hold on
plot(x1,F(x1),'r')
hold off

F = 
     Linear model Poly9:
     F(x) = p1*x^9 + p2*x^8 + p3*x^7 + p4*x^6 + 
                    p5*x^5 + p6*x^4 + p7*x^3 + p8*x^2 + p9*x + p10
     Coefficients (with 95% confidence bounds):
       p1 =    9.68e-15  (-3.893e-15, 2.325e-14)
       p2 =   -4.35e-12  (-1.053e-11, 1.827e-12)
       p3 =   7.335e-10  (-4.463e-10, 1.913e-09)
       p4 =  -5.364e-08  (-1.764e-07, 6.914e-08)
       p5 =    9.72e-07  (-6.588e-06, 8.532e-06)
       p6 =    8.03e-05  (-0.0001994, 0.00036)
       p7 =   -0.004159  (-0.01019, 0.00187)
       p8 =     0.05116  (-0.01818, 0.1205)
       p9 =      0.1133  (-0.236, 0.4626)
       p10 =      0.3849  (-0.09655, 0.8663)

[Severin Handelshauser]

Thanks, actually I wanted to put together the output file myself. But what this function outputs is almost the way I wanted it to be.

[Severin Handelshauser]

Do you know which regression algorithm that is?

[darova]

have no idea