Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 207 / 4 / d / iv

The residual plot has two asymmetric clouds. Event residuals lie below the horizontal boundary $1$, while censored residuals lie at or below $0$. Because $\hat{\beta }>0$, fitted cumulative hazard contains the rapidly increasing multiplier $e^{\hat{\beta }z}$; individuals with large $z$ who remain event-free until censoring can therefore have very negative residuals. At small $z$, events tend to lie near $1$ and censored observations near $0$. The resulting scatter is wedge-shaped and increasingly spread toward negative values as $z$ grows, rather than homoscedastic or approximately normal.