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));
J = 1/(2*m)*sum((X*theta-y).^2)+lambda/(2*m)*(sum(theta.^2)-theta(1).^2);
 
grad = 1/m*X'*(X*theta-y)+lambda/m*theta;
grad(1) = grad(1) -lambda/m*theta(1);
% ====================== 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.
%












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

grad = grad(:);

end
