cost_logisticV3.m

function [cost, gradient] = cost_logisticV3(a, x, y)
% cost_logisticV3 Compute cost and gradient for logistic regression
%   cost = cost_logistic(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.

% ====================== YOUR CODE HERE ======================
% Compute the cost of a particular choice of a. Compute the partial derivatives and set grad to the partial derivatives of the cost w.r.t. each parameter in theta

cost = 0;       %initialize values
gradient = 0; %initalize a gradient
t = a(1).*(x.^0)+a(2).*x;  %time function
sigma = 1./(1+exp(-t));    %calculate sigma
cost = sum(-y.*log(sigma)- (1-y).*log(1-sigma)); %Calculation of cost
costFunction = @ (a) sum(-y.*log((1./(1+exp(-(a(1)+a(2).*x)))))-(1-y).*log(1-(1./(1+exp(-(a(1)+a(2).*x))))));
gradient = (1/length(x))*sum((sigma-y).*t); %Calculation of gradient
ai = [0 0]; %initialize a value for a

%---------------------- Plot of Regression -----------------------------
plot(x,y,'x', x, sigma);
title('Regression')
xlabel('Temp (Degrees Fahrenheit)')
ylabel('Pass or Fail (1 or 0)')

end