Regression isn't only a prediction tool. Analysts use it to estimate how outcomes relate to several factors at once.
Controlling for Factors
A regression of salary on education, experience and industry estimates the relationship with each factor holding the others constant. This helps separate overlapping influences — though only for factors you include.
Interpreting Coefficients
- For a numeric variable: the expected change in the outcome for a one-unit increase, other things equal.
- For a category: the difference compared with a reference category.
- For a log-transformed outcome: approximately a percentage change.
Uncertainty
Each coefficient comes with a standard error and confidence interval. A coefficient whose interval spans zero is not clearly different from no relationship.
Diagnostics
- Residual plots: check for curves or funnels that break assumptions.
- Influential points: a few observations can drive results.
- Multicollinearity: highly correlated predictors make individual coefficients unstable.
Common Pitfalls
- Interpreting coefficients causally without a causal design.
- Omitting important confounders.
- Extrapolating beyond the data's range.
- Including variables that are consequences of the outcome.
Tools
import statsmodels.formula.api as smf
model = smf.ols("salary ~ education + experience + C(industry)", data=df).fit()
print(model.summary())
Communicating Results
Translate coefficients into plain statements with uncertainty, and be explicit about what the analysis can and can't show.