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When a full-rank normal regression with positive residual degrees of freedom happens to fit all supplied observations exactly, its residual estimate of variance is zero. The ordinary Studentized prediction-interval formula formally collapses, but the statistic divides by zero. Under positive true Gaussian variance such samples form a null set; exact rounded or constructed data must not be treated as proof that future randomness vanishes.

If a random variable has variance zero and mean $m$, it equals $m$ almost surely. For a target probability strictly between zero and one, $\mathbb{P}(X\ge C)$ meets the target exactly when $m<C$. Substituting zero variance into a positive-variance non-strict quantile constraint incorrectly includes $m=C$, where the overflow probability is one. The distinction comes from the atom at the threshold.