linearRegCostFunction.m

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.
%

    vec = X*theta-y;
    J = (1/(2*m)) * vec' * vec;
    nobias_theta = theta;
    nobias_theta(1) = 0; 
    
    J = J + (lambda/(2*m)) * nobias_theta' * nobias_theta;

    grad = (1/m) * (X' * vec) + (lambda/m) * nobias_theta;








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

grad = grad(:);

end