function [J, grad] = costFunction(theta, X, y)
%COSTFUNCTION Compute cost and gradient for logistic regression
%   J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the
%   parameter for logistic regression and the gradient of the cost
%   w.r.t. to the parameters.

% 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 of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta
%
% Note: grad should have the same dimensions as theta
%

pred = sigmoid(X*theta);

% J = 1 /m .* sum(-y .* log(pred) - (1-y) .* log(1-pred));

% grad = 1 / m .* (X' * (pred - y));

J = (1 / (2*m)) * sum((pred - y).^2);

grad = (1 / m) * X' * (pred - y);

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

end