function [h,sig] = ztest(y,X,omega,Omega,alpha)
%FTEST  Hypothesis test.
%   [H,SIG] = FTEST(Y,X,omega,OMEGA,ALPHA) performs an F-test to determine
%   whether a linear model defined by omega is sufficient compared to
%   the model defined by OMEGA.
%   Y contains the response variables, X the explanatory variables and
%   OMEGA, omega are subsets of the rows of X. omega is a subset of OMEGA.
%   ALPHA = 0.05 by default.
%
%   The null hypothesis is: "omega is the true model".
%
%   ALPHA is the desired significance level. 
%   SIG is the probability of observing the given result by chance
%   given that the null hypothesis is true. Small values of SIG cast
%   doubt on the validity of the null hypothesis.
%
%   H=0 => "Do not reject null hypothesis at significance level of alpha."
%   H=1 => "Reject null hypothesis at significance level of alpha."

%   Copyright (c) 2000 by Reinhard Furrer.

%   Parameter verification
if nargin < 3, 
    error('Requires at least three input arguments.'); 
end

[n,m] = size(X);
[n1,collhs] = size(y);
if n ~= n1, 
    error('The number of rows in Y must equal the number of rows in X.'); 
end 

if collhs ~= 1, 
    error('Y must be a vector, not a matrix'); 
end
omega=unique(omega);
[m1 q] = size(omega);
if (m1 ~= 1 & q ~= 1) 
    error('Invalid variable selection.');
end

if nargin < 4,
  Omega=[1:m];
  p=m;
else
  Omega=unique(Omega);
  [m1 p] = size(Omega);
  if (m1 ~= 1 & p ~= 1 & p > q & max(Omega)>m ) 
    error('Invalid variable selection.');
  end
end

oX=X(:,intersect(omega,Omega));
OX=X(:,Omega);

if nargin < 5, 
    alpha = 0.05; 
end 

%   Actual Fobs calculation

[b,bint,Or] = regress(y,OX);
[b,bint,or] = regress(y,oX);
Osc=sum(Or.^2);
osc=sum(or.^2);

Fobs=(osc-Osc)/(Osc)*(n-p)/(p-q);
sig=finv(Fobs,p-q,n-p);


if (alpha <= 0 | alpha >= 1)
    fprintf('Warning: significance level must be between 0 and 1\n'); 
    h   = NaN;
    sig = NaN;
    return;
end


% Determine if the actual significance exceeds the desired significance
h = 0;
if sig <= alpha, 
    h = 1; 
end 

if isnan(sig), 
    h = NaN; 
end