%-----------------------------------------------------
%
% Matlab script corresponding to a hill height problem.
% Set up was:  
%  
% From ground level,
%   A is measured 1236 meters high
%   B is measured 1941 meters high
%   C is measured 2417 meters high
%  
% From A, B is  711 meters higher 
% From A, C is 1177 meters higher 
% From B, C is  475 meters higher 
%  
% This file differs from hills1.m only by lining up  
% the elements in defining the string s, so that any  
% typos or errors is easier to spot.  
%  
%-----------------------
%
% Started  : 11 Jan 2009
% Modified : 24 Feb 2009, to correct the last statement
%   of the last observation from A -> B to B -> C.
%
%-----------------------------------------------------

G = [ 1  0 0
      0  1 0
      0  0 1
      -1 1 0
      -1 0 1
      0 -1 1];

b = [1236; 1941; 2417; 711; 1177; 475];

[number_of_observations, number_of_parameters] = size(G);

h = G\b;

r = b - G*h;
disp('residual (error) vector = ');
disp(r);

s = ['Best least squares fit for data is height(A) = ', num2str(h(1)), ...
                                      ', height(B) = ', num2str(h(2)), ...
                                      ', height(C) = ', num2str(h(3))];
disp(s);
    
[outlier, outlier_index] = max(abs(r));
s = ['Worst outlier is observation ', num2str(outlier_index)];
disp(s);