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