% 
% Written by:
% -- 
% John L. Weatherwax                2009-04-21
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

close all; drawnow; clear functions; 
rehash; 
clc; 

[X,Y] = load_narula_wellington(); n = size(X,1); alpha = 0.05; 

% prepend a column of zeros for the constant term: 
X = [ ones(n,1), X ]; 

% begin with a regression model consisting of ALL variables: 
%
[beta,sC,s_hat,t_stats,SSE,SSR,SSTO,R2,MSR,MSE,F_ratio,MI] = wwx_regression(X,Y,1); 

% drop the variable X_2: 
X(:,2+1) = []; 
[beta,sC,s_hat,t_stats,SSE,SSR,SSTO,R2,MSR,MSE,F_ratio,MI] = wwx_regression(X,Y,1); 

% drop the variable X_4: 
X(:,4) = []; p = 2; 
[beta,sC,s_hat,t_stats,SSE,SSR,SSTO,R2,MSR,MSE,F_ratio,MI] = wwx_regression(X,Y,1); 

% evaluate the sale price of this house:
x = [ 1, 10.0, 1.5 ]; 

y_hat = (x) * beta; 

s2 = MSE; 
s  = sqrt(MSE); 
t_value = tinv( 1-0.5*alpha, n-p-1 );

% the prediction interval is given by: 
y_hat + t_value * s * sqrt( ( 1 + x * (MI * x.') ) ) * [ -1, +1 ]