Checked content

File:Linear least squares.svg

Description Illustration of linear least squares.
Date 19:15, 2 February 2008 (UTC)
Source self-made with MATLAB, tweaked in Inkscape.
Author Oleg Alexandrov
Matlab Logo.png
 This chart 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) 

% 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 = 18; % font size
   figure(1); clf; hold on;
   set(gca, 'fontsize', fs);
   set(gca, 'linewidth', lw/2.5)
   hold on; grid on;
 
   % random numbers
   a = 1.1; b = 3.5; 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*0.4*erfinv(2*rand(1) - 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, colour)
   Theta=0:0.1:2*pi;
   X=r*cos(Theta)+x;
   Y=r*sin(Theta)+y;
   H=fill(X, Y, colour);
   set(H, 'EdgeColor', 'none');


|lang1=en|wiki1=wikipedia|article1=Linear_regression |lang2=it|wiki2=wikipedia|article2=Minimi_Quadrati |gallery1=Control theory }}

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