function J = computeCostMulti(X, y, theta)

	m = length(y); % number of training examples
	J = 0;
	predictions = X * theta;
	J = 1/(2*m)*(predictions - y)' * (predictions - y);

end

function [theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters)

	m = length(y); % number of training examples
	J_history = zeros(num_iters, 1);
	feature_number = size(X,2);
	temp = zeros(feature_number,1);
	for iter = 1:num_iters

		for i=1:feature_number
			temp(i) = theta(i) - (alpha / m) * sum((X * theta - y).* X(:,i));
		end
		for j=1:feature_number
			theta(j) = temp(j);
		end
	 
		J_history(iter) = computeCostMulti(X, y, theta);

	end

end

function [X_norm, mu, sigma] = featureNormalize(X)

	X_norm = X;
	mu = zeros(1, size(X, 2));
	sigma = zeros(1, size(X, 2));
	mu = mean(X);
	sigma = std(X);
	for i=1:size(mu,2)
		X_norm(:,i) = (X(:,i).-mu(i))./sigma(i);
	end

end

function [theta] = normalEqn(X, y)

	theta = zeros(size(X, 2), 1);
	theta = pinv(X'*X)*X'*y;

end