% Linear regression with arbitrary points, universal program, easy to add extra points
% Both theta0 and theta1 are updated simultaneously.

clear
clc

x = [1 2 3];
y = [1 2 3];
myData = [x; y]';

theta0 = -2 : 0.1 : 5;
theta1 = -2 : 0.1 : 5;

Jtheta01 = zeros(length(theta1));
for i1 = 1 : length(theta0)
    for i2 = 1 : length(theta1)
        temp = 0;
        for j = 1 : length(x)
            temp = temp + (theta0(i1) + theta1(i2) * myData(j,1) - myData(j,2))^2;
        end
        Jtheta01(i1,i2) = (1/(2*length(x))) * temp;
    end
end

% [X, Y] = meshgrid(theta0, theta1);
% mesh(X,Y,Jtheta01)
% q=inf;
% % 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