Polyfit is giving incorrect coefficients for correct plot fit.

So when using polyfit I get a really nice line ploted and matches my data well. Unfortunately when I go to use the coefficients determined by polyfit, it doesn't make sense at all! My expected slope c(1) is around 0.3 but I'm getting around 6. Even when I do the approximate calculation of the slope by hand it is as expected so my data mustn't be wrong.

Here's my code...

N=10:10:60;
t1 = [3.5 6.5 10 12.5 15.5 19];
t2 = [3 6.5 10 13 16 20];
t3 = [3 7 10.5 13.5 17 20];
t4 = [4 7 10 13 16.5 20];
t5 = [3.5 7 11 14.5 18 20.5];
T = [t1;t2;t3;t4;t5];
m = mean(T);

%Linear fit using polyfit
[c,S,mu] = polyfit(N,m,1);
%Error values of coefficients
ci = polyparci(c,S);
% Display evaluated equation y = m*x + b and the wavelength (desired to be approx. 0.6 micrometers)
disp(['Equation is y = ' num2str(c(1)) '*x + ' num2str(c(2))])
disp(['Wavelength is ' num2str(2.*c(1)) ' micrometers'])
% Evaluate fit equation using polyval
[y_est, delta] = polyval(c,N,S,mu);
%Polyfit function from coefficients 
f = c(1)*N + c(2);

hold on

%Plotting of data
scatter(N,m,'b')
%Plotting of linear fit from polyval
plot(N,y_est,'r')
%Plotting of linear fit from function with coefficients
plot(N,f,'g')
%Labelling axes and plot etc...

hold off

I've added a plot of the function of the function with the coefficients

f = c(1)*N + c(2);
plot(N,f,'g')

to show how they are incorrect. This is the plot it outputs.

I thought I used polyfit correctly but I must not have. Where have I gone wrong?

Answer 1

[Stijn Haenen]

If I run this script i get a good fit, see image

N=10:10:60;
t1 = [3.5 6.5 10 12.5 15.5 19];
t2 = [3 6.5 10 13 16 20];
t3 = [3 7 10.5 13.5 17 20];
t4 = [4 7 10 13 16.5 20];
t5 = [3.5 7 11 14.5 18 20.5];
T = [t1;t2;t3;t4;t5];
m = mean(T);

[c] = polyfit(N,m,1);

f = c(1)*N + c(2);
plot(N,f,'g')
hold on
scatter(N,m,'b')

[N O'SS]

Ah it worked when I removed the mu from the equation and it worked. Why does that happen? I thought mu just helps with calculating the error, but as I removed it the errors still worked.

Thank you for your help!