% INTERACTIVE DUMMY VARIABLES & SPLINE REGRESSIONS IN AN EARNINGS EQUATION 
clc;

% Load Data 
M = importdata('matlabex11data.txt');
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);
margrade = married.*grade;
constant = ones(n,1);
xmat = [constant,age,age2,grade,married,margrade];
k = size(xmat,2);
spline = 1;

% ******************** 
% DUMMY VARIABLE MODEL 
% ******************** 

if spline == 0;
	
% Least Squares Estimation 
b = inv(xmat'*xmat)*(xmat'*lnwage);
e = lnwage - xmat*b;
s2 = e'*e/(n-k);
varb = s2*inv(xmat'*xmat);
t = b./sqrt(diag(varb));
disp(['Unrestricted Coefficient Vector = ']); 
disp(num2str(b));
disp([' ']);
disp(['t Statistics = ']); 
disp(num2str(t));
disp([' ']);

% Graph Fitted Regression Line (Married=0) 
grade = linspace(8,18,n)';
age = 25*ones(n,1);
age2 = (25.^2)*ones(n,1);
constant = ones(n,1);
null = zeros(n,1);
margrade = grade.*null;
married = zeros(n,1);
xmat = [constant,age,age2,grade,married,margrade];
lnwage0 = xmat*b;

% Fitted Regression Line (Married=1) 
married = ones(n,1);
margrade = grade.*constant;
xmat = [constant,age,age2,grade,married,margrade];
lnwage1 = xmat*b;

plot(grade,[lnwage0,lnwage1]);
title('Predicted lnwage of Married & Unmarried Evaluated at Age=25');
xlabel('Grade');
ylabel('lnwage'); 

% ***************** 
% SPLINE REGRESSION 
% ***************** 

else;
	
% Least Squares Estimation 
d12 = grade > 12;
d16 = grade > 16;
gradeless12 = d12.*(grade-12);
gradeless16 = d16.*(grade-16);
xmat = [constant,age,age2,grade,gradeless12,gradeless16,married];
k = size(xmat,2);
b = inv(xmat'*xmat)*(xmat'*lnwage);
e = lnwage - xmat*b;
s2 = (e'*e)/(n-k); 
varb = s2*inv(xmat'*xmat);
t = b./sqrt(diag(varb));
disp(['Unrestricted Coefficient Vector = ']); 
disp(num2str(b));
disp([' ']);
disp(['t Statistics = ']); 
disp(num2str(t));
disp([' ']);

% Graph Spline Regression  
grade = (8:0.02:(8+0.02*(n-1)))';
d12 = grade > 12;
d16 = grade > 16;
gradeless12 = d12.*(grade-12);
gradeless16 = d16.*(grade-16);
age = 25*ones(n,1);
age2 = (25.^2)*ones(n,1);
xmat1 = [constant,age,age2,grade,gradeless12,gradeless16,zeros(n,1)];
lnwagehat = xmat1*b;

title('Spline Regression of lnwage--Evaluated at Age=25 & Married=0');
xlabel('Grade');
ylabel('lnwage'); 
plot(grade,lnwagehat);

%Hypothesis Test for Constant Slope 
R1 = [0 0 0 0 1 0 0];
R2 = [0 0 0 0 0 1 0];
R = [R1;R2];
q = [0;0];
F = (R*b - q)'*inv(R*inv(xmat'*xmat)*R')*(R*b - q)/(2*s2);
disp(['F Statistic = ' num2str(F')]);
end