When writing the relations in a causal diagram, an arrow indicates a causal function of the input variables mapping to the output variable. The absence of an arrow indicates the absence of a causal function mapping those variables to one or the other.

In this new context, we can write an explicit function of variables to model an outcome variable, but we are doing so with a strict “structural” assumption, that our model is the model occuring in nature. When we run a linear regression in this context we already know that X, Z cause Y. The regression will now tell us how.

By varying the input variables, we are assessing the many alternate worlds that occur by changing what we have observed.