%% Problem 1 on the take home exam.

%  I'm giving you some partial commands below so that you can just fill
%  them in and run the code-  Note that the code will not run correctly
%  until you do fill them in.
%

% Be sure and download the Matlab data file to a directory with this m-file

load Exam1THQ1;  % This loads X (100 x 3) and Xtest (10 x 2).

%% Set up the matrix for the least squares problem as Ax = b
%
% Think about it column-wise, where the x's are in the first column, X(:,1), 
%  the y's are in the second column, X(:,2), and the z's (the outputs) 
%  are in the third column, X(:,3).

A=[     ];  % Fill this command in - As a hint, A should be 100 x ?
b=X(:,3);   % I'll give you this one
xhat= ;     % Fill this command in - This is the least squares solution

% If A was correctly assembled above, this line should work without change.
Atest=[Xtest(:,1).^2, Xtest(:,1).*Xtest(:,2), Xtest(:,2), sin(Xtest(:,2)), ones(10,1)];
z=Atest*xhat



%%