Trouble using polyfit that separated straight fit from original data points

Hi all,

I am plotting some data from a power-inverse law and using the following:

loglog(E2dist,E2PrdB,'+g'), hold on

p = polyfit(log(E2dist),log(E2PrdB),1);

m = p(1);

b = exp(p(2));

%mean=mu(1);

%std=mu(2);

loglog(E2dist, b.*E2dist.^m,'-m*');

This works fine. But when I change to

[p,S,mu] = polyfit(log(E2dist),log(E2PrdB),1);

my straight line fit is separated vertically from my original data points?

Hope you can help.

cheers

Answer 1

[dpb]

From

doc polyfit

[P,S,MU] = polyfit(X,Y,N) finds the coefficients of a polynomial in
  XHAT = (X-MU(1))/MU(2) where MU(1) = MEAN(X) and MU(2) = STD(X).

It's a "feature" that's non-intuitive, indeed. Would seem to have been better to use a flag to ask for/control centering rather than just the form of the output.

Answer 2

[Image Analyst]

When you use polyval() to get your estimated x values, you need to pass in S and mu to get values in your original range. See this demo:

x = -10:10;
y = x + 10 + 20*rand(1, length(x));
plot(x,y,'bd-', 'LineWidth', 3, 'MarkerSize', 15);
ylim([0 40]);
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
grid on;

% Fit a line to the noisy data
[coefficients, S, mu] = polyfit(x, y, 1);
% Get the fit.  YOU NEED TO PASS IN S AND MU!
yFitted = polyval(coefficients, x, S, mu);
% Plot it
hold on;
plot(x,yFitted,'r*-', 'LineWidth', 3, 'MarkerSize', 15);

[James]

This is an equally good answer too! thanks.