% linear regression with 3 points
% Not universal, just to see the method

clear
clc

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

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

Jtheta1 = zeros(1, 41);

for i = 1 : 41
    temp = 0;
    for j = 1 : 3
        temp = temp + (theta0 + theta1(i) * myData(j,1) - myData(j,2))^2;
    end
    Jtheta1(i) = (1/6) * temp;
end

subplot(1,2,1), plot(x,y,'s', 'markerSize',12, 'markerFaceColor','b'), ...
    xlabel('x'), ylabel('y'), axis([0.8 3.2 0.8 3.2]), grid on, hold on, line(x,y,'LineWidth',3)
subplot(1,2,2), plot(theta1, Jtheta1,'LineWidth',3), xlabel('theta 1'), ylabel('J(theta 1)'), grid on