The linear variance conjecture for signatures of 2-bridge knots

Let $T(c)$ be the set of objects with crossing number $c$ considered in the paper, and let the variance of their signatures be computed with respect to the uniform distribution on $T(c)$. Linear variance conjecture. The variance over $T(c)$ for crossing number $c$ is approximately

$$c-5+.336.$$

The numerical tables for even and odd crossing numbers suggest an approximately linear growth law, but no proof or resolution is supplied here.