%% Get some data together
x=rand(13,1);
x=sort(x);
y=2*randn(size(x));
plot(x,y,'.')

t=linspace(0,1);  % 100 evenly spaced points between 0 and 1


%% Form the Vandermonde matrix (starting with the highest power in the first column)
vv=vander(x');

% Find the polynomial coefficients by just inverting the Vandermonde matrix
c1=inv(vv)*y;
y1=polyval(c1,t);  %Evaluate the polynomial using coefficients in c1 on data in t.

hold on
plot(t,y1,'k-');  %Plot the result
%axis([0 1 -40 40])  %Probably need to re-scale


[U,S,V]=svd(vv);  %Let's see what happens with the pseudo inverse.
c5=V(:,1:8)*diag(1./diag(S(1:8,1:8)))*U(:,1:8)'*y
y2=polyval(c5,t);
plot(t,y2,'r-');
hold off