Reading Regression Output

Read regression output by connecting each coefficient to the model's units and specification, interpreting its uncertainty, and checking diagnostics and study design. R-squared summarizes fit; a p-value concerns incompatibility with a stated null model.

A regression table summarizes a fitted relationship under a particular specification. A coefficient's interpretation depends on units, included predictors, interactions, and transformations. Its uncertainty depends on assumptions about sampling and errors. Read the model and study design before treating a coefficient as an actionable effect.

A p-value describes how incompatible a test statistic is with a specified null model, using outcomes at least as extreme under that model. It is not the probability that the coefficient is real or that the null is true. R-squared describes in-sample fit for the chosen model and outcome; useful prediction and causal interpretation require additional evidence.

When to use it

When regression analysis needs proper interpretation; when the distinction between statistical significance and practical importance matters; when understanding that association ≠ causation in regression output; when residual analysis would reveal model limitations.

How it can help

Inspect the specification and sampling first, then coefficient magnitude, uncertainty, practical relevance, and diagnostics. Use suitable validation for prediction and a separate causal argument for intervention decisions.