The $X_1$ coefficient is the total causal effect of $X_1$ on $Y$. The node $X_1$ has no parents, so there is no <backdoor path> into it, and the unadjusted regression sums all directed paths from $X_1$ to $Y$.

Solution

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

A backdoor path from exposure $X$ to outcome $Y$ begins with an arrow entering $X$. An adjustment set identifies the total effect when it blocks every such path without conditioning on descendants of $X$.


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 Incoming links: Backdoor path