% Illustration of linear least squares.
function main()
 
   % KSmrq's colors
   red    = [0.867 0.06 0.14];
   blue   = [0, 129, 205]/256;
   green  = [0, 200,  70]/256;
   yellow = [254, 194,   0]/256;
   white = 0.99*[1, 1, 1];
   gray = 0.1*white;
 
% Set up the grid and other parameters
   Xr = [-1, 0, 2, 4];
   Yr = [3   6  8  9];
   
   N = 100;
   small = 0.2;
   X = linspace(min(Xr)-4*small, max(Xr)+4*small, N);
   C=-4; D = 4;
 
   % 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;
 
   % random numbers
   s=0.16;
   a = 1.2; b = 3; c = 1;
   p = 1; q = 6.5; r = 1.3;
   M = 50;
   p = s*p; q = s*q; r = s*r;

   myrad = 0.1;
   for i=1:length(Xr)
      ball(Xr(i), Yr(i), myrad, red);
   end

   axis equal;
 
 
   % least squares fitting
   Yr = Yr';
   Xr=Xr';
   Mat = [(0*Xr+1) Xr];
   V=Mat'*Yr;
   V=(Mat'*Mat)\V;
   pe = V(1); qe = V(2);
   
   plot(X, pe+qe*X, 'b', 'linewidth', lw);
 
   grid on;
   set(gca, 'GridLineStyle', '-', 'xcolor', gray);
   set(gca, 'GridLineStyle', '-', 'ycolor', gray);
   set(gca, 'XTick', min(Xr):1:max(Xr));
 
   axis equal;
   axis([min(Xr)-2*small max(Xr)+2*small min(Yr)-2*small max(Yr)+4*small]);
 
   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')