Linear Regression

costFunction.m

function J = costFunction(X, y, theta)
  % Compute cost for linear regression
  %   J = costFunction(X, y, theta) computes the cost of using theta as the
  %   parameter for linear regression to fit the data points in X and y

  % Initialize some useful values
  m = length(y); % number of training examples
  % Compute the cost
  J = sum((X * theta - y).^2) * 1/(2*m);
  % =========================================================================
end

gradientDescent.m

function [theta, J_history] = gradientDescent(X, y, theta, alpha, iterations)
  %GRADIENTDESCENT Performs gradient descent to learn theta
  %   theta = GRADIENTDESCENT(X, y, theta, alpha, iterations) updates theta by 
  %   taking iterations gradient steps with learning rate alpha

  % Initialize some useful values
  m = length(y); % number of training examples
  J_history = zeros(iterations, 1);

  for iter = 1:iterations

      % ====================== YOUR CODE HERE ======================
      % Instructions: Perform a single gradient step on the parameter vector
      %               theta. 
      %
      % Hint: While debugging, it can be useful to print out the values
      %       of the cost function (computeCost) and gradient here.
      %
      error = (X * theta - y); % h(x) - y [97x1]
      delta1 = sum(error .* X(:,1));
      delta2 = sum(error .* X(:,2));
      theta(1) = theta(1) - alpha / m * delta1;
      theta(2) = theta(2) - alpha / m * delta2;

      % ============================================================

      % Save the cost J in every iteration    
      J_history(iter) = computeCost(X, y, theta);

  end
end