cost_logistic.m

function [J, grad] = cost_logistic(a, x, y)

N = length(y); 
J = 0;
grad = 0;
t = a(1)+a(2).*x;
sigm = 1./(1+exp(-t));


J = sum(-y.*log(sigm)- (1-y).*log(1-sigm));

costFun = @ (a) sum(-y.*log((1./(1+exp(-(a(1)+a(2).*x)))))- (1-y).*log(1-(1./(1+exp(-(a(1)+a(2).*x))))));

grad = (1/length(x))*sum((sigm - y).*t);

initial = [0 0];
% Set options for fminunc
options = optimset('GradObj', 'on', 'MaxIter', 400);
% Run fminunc to obtain the optimal theta
% This function will return theta and the cost
[theta, cost] = fminunc(costFun, initial);
fminunc(@(a)(costFunction(a, x, y)), initial, options);
tt = theta(1)+theta(2).*x;
sigmm = 1./(1+exp(-tt));
setdefaults 
plot(x,y,'o', x, sigmm);
title('Best fit regression model')
xlabel('Temp (F)')
ylabel('Pass/Fail (0,1)')


end