Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 221 / 1 / b / v / Solution

Neither coefficient has a causal interpretation. Conditioning on $X_3$ opens the collider bias path $X_1\to X_3\leftarrow U\to Y$ for the $X_1$ coefficient, while the $X_3$ coefficient remains confounded by $U$ and by omitted $X_2$.