  We show that the problem of finding the measure supported on a compact subset
K of the complex plane such that the variance of the least squares predictor by
polynomials of degree at most n at a point exterior to K is a minimum, is
equivalent to the problem of finding the polynomial of degree at most n,
bounded by 1 on K with extremal growth at this external point. We use this to
find the polynomials of extremal growth for the interval [-1,1] at a purely
imaginary point. The related problem on the extremal growth of real polynomials
was studied by Erd\H{o}s in 1947.
