function output = ols(y,x);
%---------------------------------------------------
% PURPOSE: least-squares regression 
%---------------------------------------------------
% USAGE: output = ols(y,x)
% where: y = dependent variable vector (nobs x 1)
%        x = independent variables matrix (nobs x nvar)
%---------------------------------------------------
% RETURNS: a structure
%        output.meth  = 'ols'
%        output.beta  = bhat
%        output.stder = standard errors   
%        output.tstat = t-stats
%        output.yhat  = yhat
%        output.resid = residuals
%        output.sige  = e'*e/(n-k)
%        output.rsqr  = rsquared
%        output.rbar  = rbar-squared
%        output.dw    = Durbin-Watson Statistic
%        output.nobs  = nobs
%        output.nvar  = nvars
%        output.y     = y data vector
%---------------------------------------------------
% SEE ALSO: prt(results), plt(results)
%---------------------------------------------------

% written by:
% James P. LeSage, Dept of Economics
% University of Toledo
% 2801 W. Bancroft St,
% Toledo, OH 43606
% jlesage@spatial-econometrics.com

if (nargin ~= 2); error('Wrong # of arguments to ols'); 
else
 [nobs nvar] = size(x); [nobs2 junk] = size(y);
 if (nobs ~= nobs2); error('x and y must have same # obs in ols'); 
 end;
end;

output.meth = 'ordinary least squares';
output.y = y; output.x = x;
output.nobs = nobs;
output.nvar = nvar;

[q r] = qr(x,0);
xpxi = (r'*r)\eye(nvar);

output.beta = xpxi*(x'*y);
output.yhat = x*output.beta;
output.resid = y - output.yhat;
output.RSS = output.resid'*output.resid;
output.sige = output.RSS/(nobs-nvar);
output.covb = output.sige*xpxi;
tmp = (output.sige)*(diag(xpxi));
output.tstat = output.beta./(sqrt(tmp));
output.stder = output.beta./output.tstat;
ym = y - mean(y);
rsqr1 = output.RSS;
rsqr2 = ym'*ym;
output.rsqr = 1.0 - rsqr1/rsqr2; % r-squared
rsqr1 = rsqr1/(nobs-nvar);
rsqr2 = rsqr2/(nobs-1.0);
if rsqr2 ~= 0
output.rbar = 1 - (rsqr1/rsqr2); % rbar-squared
else
    output.rbar = output.rsqr;
end;
ediff = output.resid(2:nobs) - output.resid(1:nobs-1);
output.dw = (ediff'*ediff)/output.RSS; % durbin-watson