% hw72.m
% homework 7, question 2
% 

n=100;         % sample size
J=1000;        % number of simulations
beta = [1;1];  % true beta vector

% matrices to hold simulation draws
betadraws = NaN*ones(J,2);
s2draws = NaN*ones(J,1);

% main loop for simulation
for j=1:J,
	X = [ones(n,1) randn(n,1)];
	y = X*beta + randn(n,1).^2 -1;
	bhat = inv(X'*X)*X'*y;
	e = y-X*bhat;
	s2 = e'*e/(n-2);
	betadraws(j,:) = bhat';
	s2draws(j,1) = s2;
end;

% mean and variance of betahat
mean(betadraws)

cov(betadraws)

mean(s2draws)
% end hw72.m