File:Linear least squares.svg
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Size of this PNG preview of this SVG file: 494 × 599 pixels. Other resolutions: 198 × 240 pixels | 396 × 480 pixels | 633 × 768 pixels | 844 × 1,024 pixels | 1,688 × 2,048 pixels | 512 × 621 pixels.
Original file (SVG file, nominally 512 × 621 pixels, file size: 77 KB)
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DescriptionLinear least squares.svg | Illustration of linear least squares. | |||
Date | (UTC) | |||
Source | self-made with MATLAB, tweaked in Inkscape. | |||
Author | Oleg Alexandrov | |||
Permission (Reusing this file) |
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SVG development InfoField | ||||
Source code InfoField | MATLAB code% 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, 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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File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 04:33, 22 February 2009 | 512 × 621 (77 KB) | Oleg Alexandrov (talk | contribs) | Normal noise per Michael Hardy | |
00:58, 3 February 2008 | 412 × 523 (75 KB) | Oleg Alexandrov (talk | contribs) | tweak width | ||
20:27, 2 February 2008 | 401 × 523 (75 KB) | Oleg Alexandrov (talk | contribs) | tweak bd box | ||
19:54, 2 February 2008 | 4,609 × 5,778 (75 KB) | Oleg Alexandrov (talk | contribs) | tweak bd box | ||
19:50, 2 February 2008 | 4,609 × 5,778 (75 KB) | Oleg Alexandrov (talk | contribs) | tweak bd box | ||
19:41, 2 February 2008 | 754 × 945 (74 KB) | Oleg Alexandrov (talk | contribs) | tweak text font size | ||
19:38, 2 February 2008 | 55 × 69 (74 KB) | Oleg Alexandrov (talk | contribs) | tweak text font size | ||
19:15, 2 February 2008 | 303 × 411 (74 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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