% Read in data
dat = textread('hw1.dat');
% X is the design matrix
X = dat(:,1:2);
% y_bar is the vector of desired outputs
y_bar = dat(:,3);


%Plot the input features
close all;
figure(1);
plot3(X(:,1),X(:,2),y_bar,'.');
xlabel('x1');
ylabel('x2');
zlabel('y');
grid on;
title('Input data');

%Construct a "fake" error surface and generate a contour plot
theta1 = -10:10;
theta2 = -10:10;
theta_grid = ndgrid(theta1,theta2);

for i = 1:length(theta1),
  for j = 1:length(theta2),
    %Set the error to be the distance from the origin
    J(i,j) = theta1(i)^2 + theta2(j)^2;
  end
end

figure(2);
contour(theta1,theta2,J);
title('Error surface');