rand("seed", 6)
randn("seed", 6)
nsamples = 100;
% wygeneruj losowe wartości w dziedzinie [-10, 10]
x = interp1([0,1], [-10,10], sort(rand(nsamples,1)));
% prosta o równaniu y = 2 * x + 3 + szum
P = [2 3];
y = polyval(P,x) + randn(size(x))*5;
save linear_regression.mat [x y]
% wielomian 3ego stopnia ( -0.1*x^3 + 0.2*x^2 + 1 + szum )
P = [-0.1 0.2 0 1];
y = polyval(P,x) + randn(size(x))*15;
save polynomial3_regression.mat [x y]
% funkcja harmoniczna
y = 0.5 * sin(x + 0.6) + randn(size(x))/5;
save harmonic_regression.mat [x y]

load linear_regression.mat
A = [x ones(size(x))];
L = -y;
X= -inv(A'*A)*(A'*L)
hold on
plot (x,y,'*');
plot(x,polyval(X,x),"-")
hold off
print -djpg fig_linear.jpg
pause

load polynomial3_regression.mat
A = [x.^3 x.^2 x ones(size(x))];
L = -y;
X = -inv(A'*A)*(A'*L)
hold on
plot (x,y,'*');
plot(x,polyval(X,x),"-")
hold off
print -djpg fig_polynomial.jpg
pause