Image:Linear least squares.svg

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Linear_least_squares.svg (SVG file, nominally 412 × 523 pixels, file size: 75 KB)

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Description

Illustration of linear least squares.

Source

self-made with MATLAB, tweaked in Inkscape.

Date

19:15, 2 February 2008 (UTC)

Author

Oleg Alexandrov

Permission
(Reusing this image)

See below



Public domain I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide.

In case this is not legally possible:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.


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[edit] Source code (MATLAB)

% 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 = 0.2*white;
 
% Set up the grid and other parameters
   N = 100;
   A = -2.2; B = 2; 
   X = linspace(A, B, N);
   C=-4; D = 4;
 
   % Set up the figure
   lw = 4; % linewidth
   fs = 22; % font size
   figure(1); clf; hold on;
   set(gca, 'fontsize', fs);
   set(gca, 'linewidth', lw/2.5)
   hold on; grid on;
 
   % random numbers
   a = 1.2; b = 3; c = 1.4;
   M = 50;
   XX=linspace(A+0.3, B-0.3, M+1);
   Xr = 0*(1:M);
   Yr = Xr;
   for i=1:M
      r=rand(1);
      Xr(i) = XX(i)*r+XX(i+1)*(1-r);
      Yr(i) = a*Xr(i) + b + c*rand(1);
   end
 
   myrad = 0.05;
   for i=1:length(Xr)
      ball(Xr(i), Yr(i), myrad, red);
   end
 
 
   % least squares fitting
   Yr = Yr';
   Mat = [Xr' (0*Xr+1)'];
   V=Mat'*Yr;
   V=(Mat'*Mat)\V;
   ae = V(1); be = V(2);   
   plot(X, ae*X+be, 'b', 'linewidth', lw);
 
   grid on;
   set(gca, 'GridLineStyle', '-', 'xcolor', gray);
   set(gca, 'GridLineStyle', '-', 'ycolor', gray);
   set(gca, 'XTick', [-2 -1 0 1 2]);
 
 
   axis equal;
   axis([-2, 2, 1, 6]);
 
   %saveas(gcf, 'Linear_least_squares.eps', 'psc2'); % save as eps
   plot2svg('Linear_least_squares.svg'); % save as svg
 
 
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');

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeDimensionsUserComment
current00:58, 3 February 2008412×523 (75 KB)Oleg Alexandrov (tweak width)
20:27, 2 February 2008401×523 (75 KB)Oleg Alexandrov (tweak bd box)
19:54, 2 February 20084,609×5,778 (75 KB)Oleg Alexandrov (tweak bd box)
19:50, 2 February 20084,609×5,778 (75 KB)Oleg Alexandrov (tweak bd box)
19:41, 2 February 2008754×945 (74 KB)Oleg Alexandrov (tweak text font size)
19:38, 2 February 200855×69 (74 KB)Oleg Alexandrov (tweak text font size)
19:15, 2 February 2008303×411 (74 KB)Oleg Alexandrov ({{Information |Description=Illustration of linear least squares. |Source=self-made with MATLAB, tweaked in Inkscape. |Date=~~~~~ |Author= Oleg Alexandrov |Permission=See below |other_versions= }} {{PD)
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