% function to do pcr regression a=pcr_bj(x,y,k) saved as pcr_bj.m
% programmed by B. Joseph June 2001
%
% The program solves the set of redundant equations
%   Xa=y
% inputs to the function call are 
% X: a matrix
% y : the right hand side vector
% k : the number of principal components to be retained in the 
% PCR regression
% the function returns a vector a.

function a=pcr_bj(x,y,k)
[u,s,v]=svd(x);
ut=u(:,1:k);
vt=v(:,1:k);
st=s(1:k,1:k);
t=ut*st;
p=vt;
a=p*inv(t'*t)*t'*y;
return