The inconsistency of polyfit function

x=[1,2,3,4,5];
y=3*x.^2+7*x+12;
p1=plifit(x,y,2);
[p2,S]=polyfit(x,y,2);
[p3,S,mu]=polyfit(x,y,2);
p1
p2
p3
Why p3 not same as p2 and p1

Answer 1

[Stephan]

From the documentation:

[p,S,mu] = polyfit(x,y,n) also returns mu, which is a two-element vector with centering and scaling values. mu(1) is mean(x), and mu(2) is std(x). Using these values, polyfit centers x at zero and scales it to have unit standard deviation.

also in the related example:

Use polyfit with three outputs to fit a 5th-degree polynomial using centering and scaling, which improves the numerical properties of the problem. polyfit centers the data in year at 0 and scales it to have a standard deviation of 1, which avoids an ill-conditioned Vandermonde matrix in the fit calculation.