A reliable order
- Model and sample: outcome, predictors, interactions, transformations, reference groups, n, and exclusions.
- Coefficient table: estimates, units, standard errors, intervals, tests, and intercept meaning.
- Overall table: residual standard error, df, F test, R², and adjusted R².
- Diagnostics: residual form, variance, dependence, leverage, influence, and collinearity.
- Validation: sensitivity or held-out performance when the purpose requires it.
Coefficients
A slope is the expected outcome change for a one-unit predictor increase, holding other modeled variables fixed. A categorical coefficient compares with its reference group. An interaction makes a main coefficient conditional on the other term’s zero or reference value.
Standardized and unstandardized coefficients answer different scale questions. Do not infer importance from absolute coefficient size when units differ.
| Output row | Example | Careful reading |
|---|---|---|
| Intercept | 12.0 | Expected outcome when numeric predictors are zero and categories are at reference levels; it may be outside a meaningful range. |
| X coefficient | 2.4 | Expected outcome change per one X unit, conditional on the other modeled terms. |
| Group B | −3.1 | Conditional difference from the named reference group. |
| X × Group B | 1.2 | Difference in the X slope for Group B; main effects are now conditional. |
Read the interval before the p-value. A coefficient can be precisely estimated yet practically small, or uncertain across substantively different values. A p-value does not supply the effect’s direction, units, or plausibility.
Fit and tests
The overall F test asks whether the stated model improves on an intercept-only reference under assumptions. R-squared interpretation covers fit without a universal cutoff; r, R², and adjusted R² distinguishes the fields.
Residual standard error is in outcome units. Residual diagnostics show whether the mean and variance structure is credible. For a binary outcome and logit link, use logistic regression output instead.
Output fields that do not certify the model
A high R² can coexist with curvature, leakage, influential points, or extrapolation. A nonsignificant coefficient can reflect low information, collinearity, or an unnecessarily indirect parameterization. An overall significant F test can be driven by one term. Check the design matrix, missing-data handling, residual plots, influence measures, and whether predictions are evaluated on new data when prediction is the purpose.
For mediation, moderation, dummy variables, or transformed predictors, interpret the specific estimand produced by the stated model. The output does not independently establish a causal pathway.
A defensible reporting sentence
“Holding the other modeled predictors fixed, a one-unit increase in X was associated with 2.4 outcome units (95% CI [1.1, 3.7]). Model fit and residual diagnostics were reported separately; the coefficient was not interpreted causally from regression output alone.”