n = 1000;
x = randn(n, 1);
z = randn(n, 1);
y = x.^2 + 0.5*z;
scatter(x, y)
cov([x y])
r = corrcoef([x y])
text(-2, 8, sprintf('r=%.2f', r(1, 2)))
savefigpdf(gcf, 'nonlinearcorrelation.pdf', 15, 10);