% funtction ols provides the most basic output of linear regression analysis:
% i.e. the beta coef, std-errors, t-values, R^2 and sig^2. Since we need
% OLS repeatedly, feel free to extend this program by other parameters of
% intererest, such as F-value, Durbin-Watson or AIC. 

function [out,var,rsq,sigs]=ols(y,x); % the lhs must be in the same order as the lhs in the main file test.m

[n,k]=size(x);

xxi=inv(x'*x);

beta=xxi*(x'*y);

eps=y-x*beta;

sigs=eps'*eps/(n-k);

var=xxi*sigs;

se=sqrt(diag(var));

% out is a k x 3 matrix with the first column all beta coef, second std-errors and third the t-values
out=[beta,se,beta./se]; 

dy=y-mean(y);

rsq=1-(eps'*eps)/(dy'*dy);