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File:Linear least squares example.png

Linear_least_squares_example.png ‎(428 × 526 pixels, file size: 12 KB, MIME type: image/png)

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Description Illustration of linear least squares.
Date (UTC)
Source self-made with MATLAB
Author Oleg Alexandrov
 
This diagram was created with MATLAB.
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, 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')
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Date/TimeThumbnailDimensionsUserComment
current05:30, 22 May 2008Thumbnail for version as of 05:30, 22 May 2008428 × 526 (12 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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