How deeply does Causal Inference for Data Science cover regression coefficient?

Explains coefficient interpretation, adjustment, and path-based calculations, while stopping short of a complete treatment of model assumptions.

Regression coefficient

As explained in Causal Inference for Data Science

A regression coefficient is a parameter quantifying the change in a modeled outcome associated with a one-unit change in a predictor while other predictors are held fixed.

A regression coefficient measures how the modeled outcome changes when one predictor increases by one unit while the other included predictors remain fixed. Linear regression estimates the coefficients that best fit observed data, making the result both practical and interpretable for continuous variables. section 6.0

Airline price and demand

Suppose demand is modeled from ticket price and whether a flight occurs on a holiday. The price coefficient describes the change in booked seats associated with a one-unit price increase while holiday status stays unchanged. That interpretation is descriptive unless the model also addresses confounding: an airline might lower prices during economic crises and raise them in stronger periods, when demand is affected by other causes. section 6.0

The same coefficient can support different questions depending on the causal structure. A confounder can make the unadjusted coefficient misleading; including the confounder in Y ~ X + Z can estimate X's coefficient when the adjustment is appropriate. A mediator separates the direct effect from the total effect, whereas conditioning on a collider can create misleading correlation. Regression coefficients therefore require more than a good fit: interpret the variables and paths before treating them as causal effects. section 6.1.2 section 6.2.2

Use a regression coefficient by asking:

What outcome and predictor does it connect, and what units express a one-unit change? section 6.0
Which variables should be held fixed because they are confounders, and which should remain unconditioned because they are mediators or colliders? section 6.1.2
Does the coefficient represent a direct effect, a total effect, or merely an association? section 6.1.2

How Causal Inference for Data Science covers it

Cover of Causal Inference for Data Science

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Also explained in

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Statistics Every Programmer NeedsA regression coefficient is a parameter quantifying the modeled relationship between a predictor and a response, conditional on the other model terms.
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Machine Learning for Tabular Data: XGBoost, Deep Learning, and AIA regression coefficient is a parameter multiplying an input variable that determines its signed contribution to a linear regression model's prediction.
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Starting Data Analytics with Generative AI and PythonA regression coefficient is an estimated parameter expressing the change in a modeled outcome associated with a one-unit change in a predictor while other predictors are held constant.
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Statistics Slam DunkA regression coefficient is a fitted parameter quantifying the change in a response associated with a one-unit change in a predictor while other predictors are held constant.

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Related concepts

logitmeasures · A logit is a real-valued quantity representing an outcome’s log-odds or, in machine learning, an unnormalized model score used to derive probabilities.
parameterkind of · A model parameter is a numerical value, such as a weight or bias, that is learned or set to determine how a model computes outputs.
linear regressionproduced by · Linear regression is a statistical modeling method that estimates a continuous response as a linear combination of predictor variables and fitted coefficients.
maximum likelihood estimationproduced by · Maximum likelihood estimation is a statistical method that selects parameter values maximizing the likelihood of observed data under a specified probabilistic model.
treatment effectcontrasts with · A treatment effect is the difference in an outcome attributable to receiving an intervention or exposure rather than a comparison condition.
direct effectequivalent to · A direct effect is the portion of a causal effect transmitted along a specified direct causal path from a cause to an outcome, excluding effects through mediators.

This explainer was generated by Manning's knowledge graph from the text of Causal Inference for Data Science. The section links point to the parts of the book it draws on.