Orthogonal centered quadratic regression design ($X^{T}X=\mathrm{diag}(7,28,84)$)

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 $7,28,84$.