%ECON 671 Problem Set 1, Question 4. b)
%Hayashi p. 74 (f)
%Andrew McCallum, Jan. 28, 2008

%Clear memory, screen, and close all graphs before execution.
clear all;
clc;
close all;

%adds the path where I store my functions.
addpath('U:\Public\html\files\matlab\functions');
%set the seed so we all get the same results
rand('seed',1234);
randn('seed',1234);
%for some strange reason matlab is changing it's own seed for the uniform
%draws. i don't know why this is happening.

%Dimensions for the vectors and matrices.
n = 100;
k1 = 1;
k2 = 1;

%Generate x1 and x2 vectors.
%constant vector
x1 = ones(n,k1);
%uniform distribution over [1,2]
x2 = rand(n,1) + 1;
%eplison errors drawn iid from N(0, 2)
eps = normrnd(0,sqrt(2),n,1);

%Data Generating Process (DGP) is:
beta = [0.4; 0.9];
x = [x1, x2];
y = x*beta + eps;

plot(y(1:100,1), 'DisplayName', 'y(1:100,1)', 'YDataSource', 'y(1:100,1)'); figure(gcf)
%(f)
%define a few matrices we'll need
P1 = x1*inv(x1'*x1)*x1';
M1 = eye(n,n) - P1;
x2tilda = M1*x2;
ytilda = M1*y;

%(1) regress ytilda on x1
%note i have multiple outputs from myols.m but i only want the first one.
[reg1b, junk, junk2, junk3] = myols(ytilda,x1);

SSR1 = (ytilda-x1*reg1b)'*(ytilda-x1*reg1b); 
temp1 = ytilda'*ytilda;
%(2) regress ytilda on x2tilda
reg2b = myols(ytilda,x2tilda);

SSR2 = (ytilda-x2tilda*reg2b)'*(ytilda-x2tilda*reg2b); 
temp2 = ytilda'*ytilda - reg2b'*x2tilda'*x2tilda*reg2b;
%(3) regress ytilda on x1 and x2
reg3b = myols(ytilda,x);

SSR3 = (ytilda-x*reg3b)'*(ytilda-x*reg3b); 
Me = ytilda - x2tilda*reg3b(2,1);
temp3 = (Me)'*(Me);

%(4) regress ytilda on x2
reg4b = myols(ytilda,x2);

SSR4 = (ytilda-x2*reg4b)'*(ytilda-x2*reg4b);
temp4 = (Me)'*(Me);