function [bols,se,t,s2] = ols2(y,X);
% PURPOSE: simple OLS regression
% INPUTS: 
%           n by 1 vector y (dependent variable)
%           n by k matrix X (explanatory variables)
% OUTPUT:   bols: k by 1 vector of regression coefficients
%		se: k by 1 vector of standard erros
%		t: k by 1 vector of t-values
%		s2: squared regression error
%
% written by: A brilliant Math week student

n=length(y);% an alternative to size(y,1) for vectors
k=size(X,2);

bols=inv(X'*X)*X'*y;
e=y-X*bols;
s2=e'*e/(n-k); 
Vb=s2*inv(X'*X); 
se=sqrt(diag(Vb));
t=bols./se;