function [J, grad] = linearRegCostFunction(X, y, theta, lambda)
%LINEARREGCOSTFUNCTION Compute cost and gradient for regularized linear 
%regression with multiple variables
%   [J, grad] = LINEARREGCOSTFUNCTION(X, y, theta, lambda) computes the 
%   cost of using theta as the parameter for linear regression to fit the 
%   data points in X and y. Returns the cost in J and the gradient in grad

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost and gradient of regularized linear 
%               regression for a particular choice of theta.
%
%               You should set J to the cost and grad to the gradient.
%

J = ((1 / (2 * m)) * sum(power((X * theta - y), 2))) + ((lambda / (2 * m)) * sum(power(theta(2 : end), 2)));
G = (lambda / m) .* theta;
G(1) = 0;
grad = ((1/m) .* X' * (X*theta - y)) + G;

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

grad = grad(:);

end
