Calculating Residuals from polyfit

I just wanted to check that I am calculating residuals correctly as I am gettign a different answer compared to mathcad. M is my matrix of data, of which I plot column 1 (x-axis) against column 5 (y axis)

I am performing both 3rd and 5th order polynomial fits

x=M(:,1);
y=M(:,5);
p3=polyfit(x,y,3);
f3=polyval(p3,x);
p5=polyfit(x,y,5);
f5=polyval(p5,x);
plot(x,f3,'b--')
plot(x,f5,'g--')
legend('Zmx','3rd','5th')

%Calc Residuals
y3=y-f3;
y5=y-f5
axes(handles.axes2)
cla
plot(x,y3,'bd--','MarkerSize', 3)
grid on
hold on
plot(x,y5,'rd--','MarkerSize', 3)
legend('3rd','5th')

Is that correct for the residuals e.g. y3 = y-f3 ?? thanks Jason

Answer 1

[Star Strider]

It looks correct to me.

[Jason]

Thankyou for confirmation

[Star Strider]

My pleasure.

What is Mathcad giving you? (I haven’t used it in a long time, and so I don’t have it available to compare.) Are the polynomial coefficients the same as those that MATLAB calculates?

[Jason]

For the 5th order polyfit,

matlab gives: p5 =

 -347.8636  390.0972 -971.9331   37.2882   -2.3688    0.0123

Mathcad gives:

-341.56157
378.81022
-964.45718
35.05398
-2.07866

[Jason]

Error on my part, I hadn't included the constant for mathcad! It now exactly matches

[Star Strider]

No worries. I was just curious as to how you managed to get different results from both. There could be slight differences depending on precision and how both deal with floating point approximation errors, but they should be close.

So apparently they’re now both giving the same results and residuals?