% Primer za linearnu regresiju sa opadanjem gradijenta
% Postavljanje linije preko 3 tacke
clear
clc

% podaci
x = [0.5 2.3 2.9 1.5 1.8];
y = [1.4 1.9 3.2 2.1 1.7];

% inicijalna pretpostavka
theta_0 = 1;
theta_1 = -1;
alpha = 0.25;
m = size(x ,2);      % broj primeraka u skupu podataka

% crtanje inicijalne linije
u = 0 : 0.1 : 3;
v = theta_0 + theta_1 * u;

plot(u,v,'LineWidth',2)
axis([0 3 0 4])
hold on
plot(x,y,'rs', 'MarkerFaceColor','r')
text(0.5, 1.7, 'A', 'FontSize', 20)
text(2.3, 2.2, 'B', 'FontSize', 20)
text(2.8, 3.5, 'C', 'FontSize', 20)
text(1.55, 2.2, 'D', 'FontSize', 20)
text(1.8, 1.9, 'E', 'FontSize', 20)

dJ_theta_0 = 1;
dJ_theta_1 = 1;
iterationCounter = 0;

while (abs(dJ_theta_0)>0.001 || abs(dJ_theta_0)>0.001)
  SSR = 0;
  for i = 1 : m
    SSR = SSR + (theta_0 + theta_1 * x(i) - y(i))^2;
  endfor
  J = (1/(2*m)) * SSR;
  dJ_theta_0 = 0;
  for i = 1 : m
    dJ_theta_0 = dJ_theta_0 + (theta_0 + theta_1 * x(i) - y(i));
  endfor
  dJ_theta_0 = dJ_theta_0 / m;
  dJ_theta_1 = 0;
  for i = 1 : m
    dJ_theta_1 = dJ_theta_1 + (theta_0 + theta_1 * x(i) - y(i))*x(i);
  endfor
  dJ_theta_1 = dJ_theta_1 / m;
  
  theta_0 = theta_0 - alpha * dJ_theta_0;
  theta_1 = theta_1 - alpha * dJ_theta_1;
  
  v = theta_0 + theta_1 * u;
  %clf
  %plot(x,y,'rs', 'MarkerFaceColor','r')
  %axis([0 3 0 4]
  %text(0.5, 1.7, 'A', 'FontSize', 20)
  %text(2.3, 2.2, 'B', 'FontSize', 20)
  %text(2.8, 3.5, 'C', 'FontSize', 20)
  %hold on
  plot(x,y,'rs', 'MarkerFaceColor','r')
  plot(u,v,'LineWidth',2)
  drawnow
  iterationCounter = iterationCounter + 1;
endwhile