% program ex_a2_2.m 
% program to demo principal component regression of the set of equations Xa=y
% written by Babu Joseph,  June 2001
% Assume that x and y are defined
echo on;
clc;
x=[1 1;2 2 ; 3 3];
y=[1 2 3]';
% first do a singular value decomposition
[u,s,v]=svd(x)
% the principal components are displayed
% the following are the singular values
s
% select number of singular values to retain for regression
%
k= input(' Enter no of singular values to retain');
% get approximation for x
% find ti, and pi

ut=u(:,1:k);
vt=v(:,1:k);
st=s(1:k,1:k);
t=ut*st;
p=vt;
% the approximation for x using the retained singular values are:
x=t*p'
% the pcr regression solution is
a=p*inv(t'*t)*t'*y