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Many students of statistics and econometrics express frustration with the way a problem known as “bad control” is treated in the traditional literature. The issue arises when the addition of a variable to a regression equation produces an unintended discrepancy between the regression coefficient and the effect that the coefficient is intended to represent. Avoiding such discrepancies presents a challenge to all analysts in the data intensive sciences. This note describes graphical tools for understanding, visualizing, and resolving the problem through a series of illustrative examples. By making this “crash course” accessible to instructors and practitioners, we hope to avail these tools to a broader community of scientists concerned with the causal interpretation of regression models.

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The study of causal inference has seen recent momentum in machine learning and artificial intelligence (AI), particularly in the domains of transfer learning, reinforcement learning, automated diagnostics, and explainability (among others). Yet, despite its increasing application to address many of the boundaries in modern AI, causal topics remain absent in most AI curricula. This work seeks to bridge this gap by providing classroom-ready introductions that integrate into traditional topics in AI, suggests intuitive graphical tools for the application to both new and traditional lessons in probabilistic and causal reasoning, and presents avenues for instructors to impress the merit of climbing the “causal hierarchy” to address problems at the levels of associational, interventional, and counterfactual inference. Finally, this study shares anecdotal instructor experiences, successes, and challenges integrating these lessons at multiple levels of education.

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