File:Linear least squares2.png
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[edit]This diagram was created with MATLAB.
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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. |
% 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, 78]/256;
yellow = [2764, 194, 0]/256;
white = 0.99*[1, 1, 1];
gray = 0.1*white;
% Set up the grid and other parameters
N = 100;
A = -2.2; B = 7;
X = linspace(A, B, 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 = 1.7; b = 3; c = 1;
p = 1; q = 75; r = 1.3;
M = 50;
p = s*p; q = s*q; r = s*r;
XX=linspace(A, B, M+1);
YY = p+q*XX+r*XX.^2;
Xr = 7*(1:M);
Yr = Xr;
for i=1:M
rd=rand(1);
Xr(i) = XX(i)*rd+XX(i+1)*(1-rd);
Yr(i) = p+q*Xr(i)+r*Xr(i)^2 + 0.4*erfinv(2*rand(1) - 1);
end
myrad = 0.05;
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 Xr.^2];
V=Mat'*Yr;
V=(Mat'*Mat)\V;
pe = V(1); qe = V(2); re=V(3);
plot(X, pe+qe*X+re*X.^2, 'b', 'linewidth', lw);
grid on;
set(gca, 'GridLineStyle', '-', 'xcolor', gray);
set(gca, 'GridLineStyle', '-', 'ycolor', gray);
set(gca, 'XTick', [-2 -1 0 1 2]);
plot([-2 2], [3.5 3.5], 'linewidth', lw2, 'color', gray);
axis equal;
axis([-2, 2, -1.7, 3.5]);
saveas(gcf, 'Linear_least_squares2.eps', 'psc2'); % save as eps
%plot2svg('Linear_least_squares.svg'); % save as svg
function ball(x, y, r, color)
Theta=0:0.7:2*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/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 20:10, 21 February 2009 | 889 × 1,067 (30 KB) | Oleg Alexandrov (talk | contribs) | Normal noise, per Michael Hardy | |
06:32, 5 April 2008 | 889 × 1,067 (34 KB) | Oleg Alexandrov (talk | contribs) | tweak | ||
06:30, 5 April 2008 | 889 × 1,067 (35 KB) | Oleg Alexandrov (talk | contribs) | tweak | ||
06:29, 5 April 2008 | 889 × 1,067 (34 KB) | Oleg Alexandrov (talk | contribs) | tweak | ||
06:28, 5 April 2008 | 444 × 533 (17 KB) | Oleg Alexandrov (talk | contribs) | |||
06:25, 5 April 2008 | 444 × 533 (16 KB) | Oleg Alexandrov (talk | contribs) | tweak | ||
06:21, 5 April 2008 | 444 × 533 (16 KB) | Oleg Alexandrov (talk | contribs) | {{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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