% Least squares polynomial fitting (following Matlab v. 6.5
% section 12 example) L Braile, March 2005
% PolynomialFitLS2.m  Same as PolynomialFitLS.m except uses
% polyfit and polyval
% enter x and y data
x = [0 .3 .8 1.1 1.6 2.3]';
y = [0.5 0.82 1.14 1.25 1.35 1.40]';
P = polyfit(x,y,2) % find coefficients of least squares quadratic
xt = [0:0.1:2.5]';
yt = polyval(P,xt); % calculate theoretical values of
% y using polyval to plot the least squares quadratic curve
yt2 = polyval(P,x); % calculate theoretical values at the x coordinates
SSE = sum((y-yt2).^2) % calculate and print SSE
plot(xt,yt,'-',x,y,'or') % plot data and LSQ quadratic curve fit
title('2nd degree polynomial least squares fit to y = b0 + b1*x +b2*x^2')
xlabel('x')
ylabel('y')