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(@(a)(costFunction(a, x, y)), initial_a, options);


tt=theta(1)+theta(2).*x;
sigmm=1./(1+exp(-tt));


setdefaults 
plot(x,y,'o', x, sigmm);
title('Best fit regression')
xlabel('Temp (F)')
ylabel('Pass/Fail (0,1)')


end