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Description 
Illustration of linear least squares. 
Date 
19:15, 2 February 2008 (UTC) 
Source 
selfmade with MATLAB, tweaked in Inkscape. 
Author 
Oleg Alexandrov 

This chart was created with MATLAB. 
Public domainPublic domainfalsefalse 

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.Public domainPublic domainfalsefalse

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, B0.3, M+1);
Xr = 0*(1:M);
Yr = Xr;
for i=1:M
r=rand(1);
Xr(i) = XX(i)*r+XX(i+1)*(1r);
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=enwiki1=wikipediaarticle1=Linear_regression lang2=itwiki2=wikipediaarticle2=Minimi_Quadrati gallery1=Control theory }}
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