% TESTING LINEAR RESTRICTIONS 

% Load Data 
clc;
M = importdata('matlabex11data.txt',' ',1);
data = M.data;
n = size(data,1);

% Define Variables 
age = data(:,1);
age2 = age.^2;
grade = data(:,3);
lnwage = data(:,6);
potexp = data(:,9);
married = data(:,5);
union = data(:,10);
constant = ones(n,1);
xmat = [constant,age,age2,grade,married,union];
k = size(xmat,2);

% Least Squares Estimation 
urb = inv(xmat'*xmat)*(xmat'*lnwage);
rb = inv(constant'*constant)*(constant'*lnwage);
urerr = lnwage - xmat*urb;
rerr = lnwage - constant*rb;
s2 = (urerr'*urerr)/(n - k);
disp(['Unrestricted Coefficient Vector = ']); disp(num2str(urb));
disp(['Restricted Coefficient Vector = ' num2str(rb)]);

% Testing Restriction #1 
R1 = [0 0 0 1 0 0];
q1 = 0;
F1 = (R1*urb - q1)'*inv(R1*inv(xmat'*xmat)*R1')*(R1*urb - q1)/s2;
disp(['F statistic for Restriction #1 = ' num2str(F1)]);

% Testing Restriction #2 
J = k - 1;
urerrsq = urerr'*urerr;
rerrsq = rerr'*rerr;
F2 = ((rerrsq - urerrsq)/J)/(urerrsq/(n - k));
disp(['F statistic for Restriction #2 = ' num2str(F2)]);

% R2 
r2 = 1 - (urerr'*urerr)/((lnwage-mean(lnwage))'*(lnwage-mean(lnwage)));
disp(['R-squared = ' num2str(r2)]);