x = [1;2;3;4;5;6;7;8;9;10;11;12];
y = [69.2; 77.5; 84.7; 86.8; 90.1; 105.9; 105.1; 107.7; 100.3; 90.0; 73.4;65.4];

plot(x,y,'o')
X = [ones(size(x)),x, x.^2, x.^3, x.^4, x.^5];
z = X'*y;
S = X'*X;
U = chol(S);
w = U'\z;
c = U\w;
q = 1:0.1:12;
fit = c(1)+c(2)*q+c(3)*q.^2+c(4)*q.^3+c(5)*q.^4+c(6)*q.^5;
hold on
axis tight
plot (q, fit,'red','linewidth', 2);
hold off
legend('data points', 'quadratic fit' , 'location' ,'northwest');
 format short e
c