% 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, 'colour', 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, colour)
Theta=0:0.7:2*pi;
X=r*cos(Theta)+x;
Y=r*sin(Theta)+y;
H=fill(X, Y, colour);
set(H, 'EdgeColor', 'none')