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File:Linear least squares example2.png

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Description Illustration of linear least squares.
Date (UTC)
Source self-made with MATLAB
Author Oleg Alexandrov
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This diagram was created with MATLAB.


Licensing edit

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Source code (MATLAB) edit 

% 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')

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Date/TimeThumbnailDimensionsUserComment
current19:51, 1 June 2008Thumbnail for version as of 19:51, 1 June 20081,245 × 1,569 (52 KB)Oleg Alexandrov (talk | contribs)Add x and y labels
04:12, 24 May 2008Thumbnail for version as of 04:12, 24 May 20081,199 × 1,476 (37 KB)Oleg Alexandrov (talk | contribs){{Information |Description=Illustration of linear least squares. |Source=self-made with MATLAB |Date=~~~~~ |Author= Oleg Alexandrov |Permission=See below |other_versions= }} {{PD-self}} ==Source code

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