  The variance of primes in short intervals relates to the Riemann Hypothesis,
Montgomery's Pair Correlation Conjecture and the Hardy--Littlewood Conjecture.
In regards to its asymptotics, very little is known unconditionally. We study
the variance of integers without prime factors below $y$, in short intervals.
We use complex analysis and sieve theory to prove an unconditional asymptotic
result in a range for which we give evidence is qualitatively best possible. We
find that this variance connects with statistics of $y$-friable (smooth)
numbers, and, as with primes, is asymptotically smaller than the naive
probabilistic prediction once the length of the interval is at least a power of
$y$.
