Polyfit does not seem to be operating correctly 2011b(7.13.0.564)

Question

Jack 2012-7-19

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关闭： MATLAB Answer Bot 2021-8-20

figure(500)
x = (0: 0.1: 2.5)';
y = erf(x); 
[p,S,mu] = polyfit(x,y,6);
BestFit = polyval(p,x);
plot(x,y,'o',x,BestFit,'x'); 
grid on;
p =
    0.0017   -0.0092    0.0016    0.0708   -0.1747    0.1822    0.9230

Correct Solution:

p =
 0.0084  -0.0983   0.4217   -0.7435  0.1471   1.1064  0.0004

This is the example from the help page for polyfit.

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Answer 1

Star Strider 2012-7-19

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If you request ‘S’ and ‘mu’ from ‘polyfit’, you need to provide them to ‘polyval’ as well.

BestFit = polyval(p,x,S,mu);

should work. To get everything you asked for from ‘polyfit’ and ‘polyval’, you can also get confidence intervals on the fitted values:

[BestFit, delta] = polyval(p,x,S,mu);

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Jack 2012-7-19

Consistency between the input and output arguments does produce consistent results from polyval, but asking for mu from polyfit produces incorrect results for p. Why should the results for p depend on the other requested outputs?

Star Strider 2012-7-20

编辑：Star Strider 2012-7-20

Requesting ‘S’ and ‘mu’ from ‘polyfit’ asks it to center and scale the x-vector before doing the fit so the fit is more accurate in some situations. Without the additional scaling parameters, ‘polyval’ calculates y-values for an uncentered and unscaled x-vector different from those ‘polyfit’ used to calculate the fit. The polynomial fit parameters are correct in this context, and will of course be different from polynomial fit parameters calculated from an uncentered and unscaled x-vector.