Linear regression with fminunc

linear_regression_with_fminunc.m

x = [1000, 2000, 4000];
y = [200000, 250000, 300000];

% given a theta_0 and theta_1, this function calculates
% their cost. We don't need this function, strictly speaking...
% but it is nice to print out the costs as gradient descent iterates.
% We should see the cost go down every time the values of theta get updated.
function distance = cost(theta)
  theta_0 = theta(1);
  theta_1 = theta(2);
  x = [1000, 2000, 4000];
  y = [200000, 250000, 300000];

  distance = 0;
  for i = 1:length(x) % arrays in octave are indexed starting at 1
    square_feet = x(i);
    predicted_value = theta_0 + theta_1 * square_feet;
    actual_value = y(i);
    % how far off was the predicted value (make sure you get the absolute value)?
    distance = distance + abs(actual_value - predicted_value);
  end
  % get how far off we were on average
  distance = distance / length(x);
end

theta = [0, 0];
opt_theta = fminunc(@cost, theta);

% plot the data and the best-fit line
figure;
set (0,'defaultaxesposition', [0.15, 0.1, 0.7, 0.7]);

% function to calculate the predicted value
function result = h(x, t0, t1)
  result = t0 + t1 * x;
end

plot(x, y, 'rx');
hold on;
plot(1000:4000, h(1000:4000, theta_0, theta_1));

% tell me how much to sell a 3000 square foot home for:
disp(h(3000, theta_0, theta_1));