Forks, chains, colliders, and regression
In this section, we will see how the properties of chains, forks, and colliders manifest themselves in regression analysis. The very type of analysis that we’ll conduct in this section is actually at the heart of some of the most classic methods of causal inference and causal discovery that we’ll be working with in the next two parts of this book.
What we’re going to do now is to generate three datasets, each with three variables, 
, 
, and 
. Each dataset will be based on a graph representing one of the three structures: a chain, a fork, or a collider. Next, we’ll fit one regression model per dataset, regressing 
on the remaining two variables, and analyze the results. On the way, we’ll plot pairwise scatterplots for each dataset to strengthen our intuitive understanding of a link between graphical structures, statistical models, and visual data representations.
