LinearRegression.m

%Remember to load X and y before running

  %init XX,yy
    XX = X;
    yy = y;

    m = size(XX,1);
    n = size(XX,2);

  %Make it a sqrt function
    XX(:,1) = sqrt(XX(:,1));

  %Normalize X
  %[XX, mu, sigma] = normalize(XX);

  %Add bias term
    XX = [ones(m, 1), XX];

  %Linear regression
    lambda = 0;

    costFunction = @(t) costGrad(XX,yy,t,lambda);

    options = optimset('MaxIter', 2000, 'GradObj', 'on');

    initial_theta = zeros(n+1,1);

    [theta, J] = fminunc(costFunction, initial_theta, options);

    theta

%Display the entire surface equation in an easily copy pastable form

    %no sqrt
    %disp([num2str(theta(1)), " + ", num2str(theta(2)), " * x + ", num2str(theta(3)), " * y"]);

    %sqrt(x)
    disp([num2str(theta(1)), " + ", num2str(theta(2)), " * sqrt(x) + ", num2str(theta(3)), " * y"]);

    %normalization
    %disp([num2str(theta(1)), " + ", num2str(theta(2)), " * (x-", num2str(mu(1)), ")/", num2str(sigma(1)) ," + ", num2str(theta(3)), " * (y-", num2str(mu(2)), ")/", num2str(sigma(2))]);