Orthogonal centered quadratic regression design
= Orthogonal centered quadratic regression design
{title2=$X^TX=\operatorname{diag}(7,28,84)$}
At symmetric design points, the columns $1$, $x$ and $x^2-\overline{x^2}$ are mutually <orthogonal>. Their squared lengths give the diagonal entries of the normal-equation <matrix> and hence separate least-squares coefficient variances. At the seven <integer> points from minus three to three, these squared lengths are $7,28,84$.