%
% Examples 9.15 and 9.17
% 
% epage 432
% 
% 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; 
clc; 

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

randn('seed',0); 

x = linspace( 0, +1, 1000 ); 

% our spatially dependent variance: 
%var = ones(size(x));     % <- a constant variance of ONE
var = 20*abs(x)+1;

% generate noise with this variance: 
noise_eps = zeros(1,length(x)); 
for ii=1:length(x),
  noise_eps(ii) = normrnd(0,sqrt(var(ii)));
end

% our dependent function "y": 
y_truth = 4*x.^3 + 6*x.^2 - 1;
y       = y_truth + noise_eps; 

%fr=figure; hold on; 

line_styles={'-',':','--'}; 
line_colors='cmk'; 
data_plt_h = []; 
res_plt_h = []; 

for ii=1:3,

  % assume we *know* the dimension of the polynomial to fit: 
  [pcoef,s] = polyfit(x,y,ii); 
  
  % evaluate this polynomial model:
  yp = polyval(pcoef,x); 
  
  % plot the residuals v.s. the fitted value yp: 
  res = y-yp; 
  figure;
  hist( res, 20 );
  xlabel( 'predictor x' ); ylabel( 'residual' ); 
  title( ['histogram residual dependence plot for a polynomial model of degree', num2str(ii)] ); 
  
  figure;
  boxplot( res );
  xlabel( 'predictor x' ); ylabel( 'residual' ); 
  title( ['residual boxplot for a polynomial model of degree', num2str(ii)] ); 
  saveas( gcf, ['../../WriteUp/Graphics/Chapter10/prob_10_3_boxplot_poly_d_',num2str(ii)], 'epsc' ); 

  figure; qqplot( res ); 
  title( ['a qq plot for the polynomial model of degree', num2str(ii)] ); 
  saveas( gcf, ['../../WriteUp/Graphics/Chapter10/prob_10_3_qq_poly_d_',num2str(ii)], 'epsc' ); 
end

clear functions;