gradientDescent.m

function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
%GRADIENTDESCENT Performs gradient descent to learn theta
%   theta = GRADIENTDESCENT(X, y, theta, alpha, num_iters) updates theta by 
%   taking num_iters gradient steps with learning rate alpha

% Initialize some useful values
m = length(y); % number of training examples
J_history = zeros(num_iters, 1);

for iter = 1:num_iters

    % ====================== YOUR CODE HERE ======================
    % Instructions: Perform a single gradient step on the parameter vector
    %               theta. 
    %
    % Hint: While debugging, it can be useful to print out the values
    %       of the cost function (computeCost) and gradient here.
Sum=[0; 0];
for s=1:m
X1=X(s, [1,2])';
p1= X(s, [1,2])*theta-y(s);
p2=p1*X1;
Sum+=p2;
end
delta=(1/m)*Sum;
theta=theta-alpha*delta;





% ================================================================

    % Save the cost J in every iteration    
    J_history(iter) = computeCost(X, y, theta);

end

end