  Suppose that $K\subset\C$ is compact and that $z_0\in\C\backslash K$ is an
external point. An optimal prediction measure for regression by polynomials of
degree at most $n,$ is one for which the variance of the prediction at $z_0$ is
as small as possible. Hoel and Levine (\cite{HL}) have considered the case of
$K=[-1,1]$ and $z_0=x_0\in \R\backslash [-1,1],$ where they show that the
support of the optimal measure is the $n+1$ extremme points of the Chebyshev
polynomial $T_n(x)$ and characterizing the optimal weights in terms of absolute
values of fundamental interpolating Lagrange polynomials. More recently,
\cite{BLO} has given the equivalence of the optimal prediction problem with
that of finding polynomials of extremal growth. They also study in detail the
case of $K=[-1,1]$ and $z_0=ia\in i\R,$ purely imaginary. In this work we
generalize the Hoel-Levine formula to the general case when the support of the
optimal measure is a finite set and give a formula for the optimal weights in
terms of a $\ell_1$ minimization problem.
