cost_logistic.m

function [cost,gradient]=cost_logistic(a,x,y)
%cost_logistics calculates the cost of the and the graident of that
%sets n to the lenght of y
n=length(y);

%uses equations given in problem statement
sigma=@(t) 1./(1+exp(-t));

   
    syms a0 a1
    t=a0+a1*x;
    % calculates the cost with the variabels a0 and a1 not plugged in
    cost = (1/n)*sum(-y.*log(sigma(t))-(1-y).*log(1-sigma(t)));
   
    %find the two gradients using the diff function 
    gradient(1)=diff(cost,a0);
   gradient(2)=diff(cost,a1);
   
   %sets a0 and a2
    a0=a(1);
    a1=a(2);
    
    %substites a0 and a2 into the cost and the graients and converts them
    %to number arrays
    cost=double(subs(vpa(cost)));
    gradient=double(subs(vpa(gradient)));
    
    %plots the data
   plot(x,y, x, sigma(a(1)+a(2)*x));
   
   
   
    



end