costFunction.m

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
%
h = X*theta;
predicions = sigmoid(h);
J = (1/m)*sum((-y.*log(predicions))-((1-y).*log(1-predicions))); 
grad(1) = (1/m)*sum(predicions-y);
for i= 2:size(theta),
  grad(i) = (1/m)*(sum((predicions-y).*X(:,i))); 
endfor






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

end