%
% Written by:
% -- 
% John L. Weatherwax                2008-02-20
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clear all; 
close all; drawnow; 
clc; 

addpath( '../../Code/eda_toolbox' ); 

randn('seed',0); 

M=50;
x = linspace( 0, +1, M ); 

% the coeffients for the model: y = beta_1       +       beta_2 * x 
%                               y = beta_coef(2) + beta_coef(1) * x  
beta_coef = [ 2, 1 ];

y = polyval( beta_coef, x ); 

s = 0.15;
y = y + s*randn(size(y)); 

fh=figure; plot( x, y, 'o' ); hold on; 

% now lets add an outlier to the end of the domain: 
%
indx=M-5; 
y(indx) = y(indx)*( 1 + 3.2 ); 
figure(fh); plot( x(indx), y(indx), '-ro', 'MarkerSize', 10, 'MarkerFaceColor', 'r' ); 

% fit a polynomial model of degree one to this data: 
%
[pcoef,s] = polyfit(x,y,1); 

fprintf('True model : \n'); 
fprintf('    y = beta_0 + beta_1 x = %10.6f + %10.6f x\n',beta_coef(2),beta_coef(1));
fprintf('Estimated model : \n');
fprintf('    y = beta_0 + beta_1 x = %10.6f + %10.6f x\n',pcoef(2),pcoef(1));

% plot the true model and the estimated one: 
%
figure(fh); plot( x, polyval(beta_coef,x), '-g' ); 
figure(fh); plot( x, polyval(pcoef,x), '-r' ); 

saveas( gcf, ['../../WriteUp/Graphics/Chapter7/prob_7_2'], 'epsc' );