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.
%


h = X * theta;
reg = (lambda / (2 * m)) * sum(theta(2:end) .^ 2);
J = (1 / (2 * m)) * sum((h - y) .^ 2) + reg;

%grad(1, 1) = (1 / m) * sum((h - y) .* X(:, 1));
%grad(2, 1) = (1 / m) * sum((h - y) .* X(:, 2)) + (lambda / m) * theta(2, 1);
%grad;

temp = (h - y)' * X;
grad = (1 / m) * temp' + (lambda / m) .* theta;
grad(1) = (1 / m) * ((h - y)' * X(:, 1));







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

grad = grad(:);

end