%% How to use a training and test set
%
% First, the original data:

N=80;  %Number of points overall
xorig=linspace(-4,7,N);
xorig=xorig(:);
yorig=sin(xorig)+0.1*randn(size(xorig));

% Set up the training and testing sets:  We'll take the test set to be 80
% percent of the data.

k=randperm(N);
k1=round(0.8*N);

xtrain=xorig(k(1:k1));
xtest=xorig(k(k1+1:N));
ytrain=yorig(k(1:k1));
ytest=yorig(k(k1+1:N));

tt=linspace(-4,7,100); %For plotting only
tt=tt';

%% Training and Testing
% 
% Only use the data in xtrain to build the polynomial

for j=1:length(xtrain)
    V=vander1(xtrain,j);
    a=V\ytrain;
%    yy=polyval(a,tt);
%    plot(xtrain,ytrain,'r*',tt,yy);
%    pause
    z=polyval(a,xtest);
    Error(j)=sum((z-ytest).^2);
end