% Linear regression with arbitrary points, universal program, easy to add extra
% points

clear
clc

x = [1.5 1 2.5 3 4.5 5 2 6];
y = [2 1 2 3 3.2 5 2 4 ];
myData = [x; y]';

theta0 = 0;
theta1 = -1 : 0.1 : 3;

Jtheta1 = zeros(1, length(theta1));
% Jtheta1=0;
for i = 1 : length(theta1)
% for theta1 = -1 : 0.1 : 3
    temp = 0;
    for j = 1 : length(x)
        % temp = temp + (theta0 + theta1*myData(j,1)-myData(j,2))^2;
        temp = temp + (theta0 + theta1(i) * myData(j,1) - myData(j,2))^2;
    end
    Jtheta1(i) = (1/(2*length(x))) * temp;
    % Jtheta1(end+1) = (1/(2*length(x))) * temp;
end

% find line
[p q] = min(Jtheta1);
k = theta1(q);
x1 = min(x) : 0.1 : max(x);
y1 = k * x1;

subplot(1,2,1), plot(x,y,'s', 'markerSize',12, 'markerFaceColor','b'), ...
    xlabel('x'), ylabel('y'), axis([min(x)-0.2 max(x)+0.2 min(y)-0.2 max(y)+0.2]), grid on, hold on, ...
    plot(x1,y1,'LineWidth',3)
subplot(1,2,2), plot(theta1, Jtheta1,'LineWidth',3), xlabel('theta 1'), ylabel('J(theta 1)'), grid on