% Illustration of linear least squares.
function main()
 
   % KSmrq's colors
   red    = [0.867 0.06 0.14];
   blue   = [0, 129, 205]/256;
   green  = [0 100 0]/256;
   green=[0 139 0]/256;
   
   yellow = [254, 194,   0]/256;
   white = 0.99*[1, 1, 1];
   gray = 0.1*white;
 
   Xr = [1, 2, 3, 4];
   Yr = round(1+1.5*Xr+4*rand(1, 4))
   %Yr = [9  13  15 14];
   Yr = [6 5 7 10];
   
   A = min(Xr)-1; B = max(Xr)+1;
   C = min(Yr)-1; D = max(Yr)+1;
   N = 100;
   small = 0.2;
   X = linspace(A, B, N);
 
 
   % least squares fitting
   Yr = Yr';
   Xr=Xr';
   Mat = [(0*Xr+1) Xr];
   V=Mat'*Yr;
   V
   Mat
   V=(Mat'*Mat)\V;
   pe = V(1); qe = V(2);

   V
   
   % Set up the figure
   lw = 5; % linewidth
   lw2 = lw/2;
   fs = 22; % font size
   figure(1); clf; hold on;
   set(gca, 'fontsize', fs);
   set(gca, 'linewidth', lw2)
   hold on; grid on;
   axis equal;
 

   grid off;

   for i=1:length(Xr)
      plot([Xr(i), Xr(i)], [Yr(i) pe+qe*Xr(i)], 'color', green, 'linewidth', 0.95*lw);
   end

   myrad = 0.12;
   for i=1:length(Xr)
      ball(Xr(i), Yr(i), myrad, red);
   end

   plot(X, pe+qe*X, 'b', 'linewidth', lw);
   
   set(gca, 'GridLineStyle', '-', 'xcolor', gray);
   set(gca, 'GridLineStyle', '-', 'ycolor', gray);
   set(gca, 'XTick', A:1:B);
   set(gca, 'YTick', C:1:D);

   
   Yr - (pe+qe*Xr)
   
   axis equal;
   axis([A B C D]);
 
   saveas(gcf, 'Linear_least_squares_example.eps', 'psc2'); % save as eps
 
 
function ball(x, y, r, color)
   Theta=0:0.1:2*pi;
   X=r*cos(Theta)+x;
   Y=r*sin(Theta)+y;
   H=fill(X, Y, color);
   set(H, 'EdgeColor', 'none')