% Test mreg.m with polynomial fit data
% Calculate LSQ straight line and quadratic,
% use ANOVA to see if quadratic is statistically
% better than the straight line fit.
% Testmreg.m L Braile 2/28/05
% enter t and y data
t = [0 .3 .8 1.1 1.6 2.3]';
y = [0.5 0.82 1.14 1.25 1.35 1.40]';
% set up the function of the form y = a0 + a1*t +a2*t^2
% the a0 term will be determined later, data normalized
% by mreg by means
X = [t  t.^2 y];  % set up X matrix for mreg
[b, SR, Tot] = mreg(X); % mreg (mult. linear regression
% function is used for ANOVA)
t1 = [0:0.1:3]; % set t values for plotting LSQ lines
p1 = polyfit(t,y,1); % linear fit
p2 = polyfit(t,y,2); % quadratic fit
y1 = polyval(p1,t1); % evaluate linear fit
y2 = polyval(p2,t1); % evaluate quadratic fit
plot(t,y,'or','markersize',12,'linewidth',3) % plot data points
set(gca,'fontsize',16,'linewidth',2)
hold on
plot(t1,y1,'-b','linewidth',2) % plot
% least squares lines
plot(t1,y2,'-k','linewidth',2)
xlabel('t-values','fontsize',16)
ylabel('y-values','fontsize',16)
title('Plot sample data, straight line and quadratic fits','fontsize',16)
hold off