pollsf(x, y, sigma, M)

function [a_fit, sig_a, yy, chisqr] = pollsf(x, y, sigma, M)
% Function to fit a polynomial to data
% Inputs -
%   x - Independent variable
%   y - Dependent variable
%   sigma - Estimate error in y
%   M - Number of parameters used to fit data
% Outputs -
%   a_fit - Fit parameters; a(1) is intercept, a(2) is slope
%   sig_a - Estimated error in the parameters a()
%   yy - Curve fit to the data
%   chisqr - Chi squared statistic
N = length(x);   % Length of data set
b = y./sigma;    % Form the vector b
for i=1:N
 for j=1:M
  A(i,j) = x(i)^(j-1)/sigma(i);  % Form the design matrix
 end
end
C = inv(A.' * A);       % Compute the correlation matrix
a_fit = C * A.' * b.';  % Compute the best fit parameters
for j=1:M
  sig_a(j) = sqrt(C(j,j));  % Find the estimated error for 
end                         % the fit parameters a(j)
% Compute chi-square statistic
yy = zeros(1,N);
for j=1:M
  yy = yy + a_fit(j)*x.^(j-1);  % yy is the curve fit
end
chisqr = sum( ((y-yy)./sigma).^2 );  % Chi-square statistic
return;