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.
%

% Add ones to the X data matrix
%X = [ones(m, 1) X];

reg = (lambda / (2*m)) *sumsq(theta(2:end));

J = 1/(2*m) * ((X * theta) - y)' * ((X * theta) - y);

J = J + reg;

%do this for the rest of the terms...
%grad = (1/m) * sum(X' * (X * theta - y)) + (lambda / m * theta);

%this is madness...
%thetaFix = theta;
%thetaFix(1) = 0;

grad = (1/m) * (X' * (X * theta - y)) + (lambda / m * theta);

%do this for theta 0
grad(1) = (1/m) * sum(X(:,1)' * (X * theta(:,1) - y));



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

grad = grad(:);

end

