% example ch19ex4.m
% illustrates use of prinicipal component regression
% illustrates effect of noise how to construct a regression estimator
load ch19ex2_reg_data
reg=ch19ex2_reg_data
m=reg(:,2)-100; % the second column is the manipulated variable
x1=reg(:,3)-200; %the first secondary measurement
x2=reg(:,4)-100; %the second secondary measurement
y=reg(:,5)-90;
% Now add some noise to the test data
noise=input('Enter maximum noise value')
dx1=x1-3.66*m+ randn(20,1)*noise;
dx2=x2-5.92*m+ randn(20,1)*noise;
dy=y-4.05*m+ randn(20,1)*noise;
% do pcr regression 
A=[dx1 dx2];
estimator=pcr_bj(A,dy,1) % calculation PC regression estimator
% Now load the test data and check Rsquared value
load ch19ex2_test_data
test=ch19ex2_test_data
m=test(:,2)-100; % the second column is the manipulated variable
x1=test(:,3)-200; %the first secondary measurement
x2=test(:,4)-100; %the second secondary measurement
y=test(:,5)-90+ randn(20,1)*noise;
dx1=x1-3.66*m+ randn(20,1)*noise;
dx2=x2-5.92*m+ randn(20,1)*noise;
dy=y-4.05*m;
A=[dx1 dx2];
error=dy-A*estimator;
norm(error)
rsquared=1-norm(error)^2/norm(dy)^2