MATLAB: Error in plotting Cost Function as a function of iterations

Question

Hello all. I've been trying to implement Linear Regression with 2 features using Gradient Descent. The Gradient Descent works well numerically leading to optimal values of the Weight matrix and continuously decreasing Cost function with increasing number of iterations. But when I try to plot the graph of J vs iterations, I don't get the desired graph. Instead, all values upto the secondlast value are zero and last value is the actual minimum value of the cost function. So how do i fix this? Here's my code:

For Gradient Descent

 function [W ,J_list] = gradDescent(W, X, y, alpha, num_iters)
m = length(y);
n = length(W);
J_list = zeros(num_iters,1);A = J_list;
T0 = 0;T1 = 0;T2 = 0;
for i=1:num_iters
  T0 = W(1) -alpha*(((X * W) -y)' * X(:, 1));
  T1 = W(2) -alpha*(((X * W) -y)' * X(:, 2));
  T2 = W(3) -alpha*(((X * W) -y)' * X(:, 3));
  W(1) = T0;
  W(2) = T1;
  W(3) = T2;
  J_list(num_iters) = costFunction(X, y, W);
  fprintf('[%.0f %.0f %.0f %.0f] \n', [W(1) W(2) W(3) J_list(num_iters)]);
end
plot(1:numel(J_list), J_list, '-b', 'LineWidth', 2);
end

For the Cost Function:

 function [J] = costFunction(X,y, W)
m = length(y); %The number of training examples
n = length(W);
J = 0;
J = J + 0.5*sum((X*W-y).*(X*W-y));
end

Here is Feature Normalization:

 function [X_norm, mu, sigma] = featureNormalize(X)
 X_norm = X;
mu = zeros(1, size(X, 2));
sigma = zeros(1, size(X, 2));
 mu = mean(X,1);
sigma = std(X,1);
for i = 1:size(X,1)
    X_norm(i,:) = (X_norm(i,:) - mu)./(sigma);
 end

And here is my main code:

 clc; clear all; close all;
data = load('data.txt');
X = data(:,1:2);
y = data(:,3);
m = length(y);
[X mu sigma] = featureNormalize(X);
X = [ones(m,1), X];
W = rand(size(X,2),1)*10;
J = costFunction(X,y,W);
iterations =500;
alpha = 0.00001;
[W,J_list] = gradDescent(W,X,y,alpha,iterations);

All help is appreciated. TIA.

Answer 1

You used the wrong index here:

J_list(num_iters) =  = costFunction(...)

the index should be i.