Direct answer
Correlation summarizes a chosen form of association, while regression models an outcome conditional on predictors; neither identifies a causal effect without a design and assumptions that address alternative explanations.
Visual explanation
One coefficient can hide different geometries
What this calculation tells you
Pearson correlation measures standardized linear association, rank correlations measure monotone ordering relationships, and regression estimates a conditional relationship under a specified model.
Define predictor and outcome roles, inspect shape and influential points, preserve the sampling unit, and separate description, prediction, and causal estimation before interpreting coefficients.
Where it is used
Research
Describe and model entered associations while separating causal questions.
Operations
Explore relationships among process measures before prediction validation.
Education
Show how identical summary coefficients can hide different geometries.
Data review
Identify nonlinearity, subgroups, time trends, and influential observations.
Common situations
- Choosing Pearson or rank correlation.
- Interpreting a regression slope.
- Investigating an influential point.
- Explaining why prediction and causation differ.
Start with the statistical question
Define predictor and outcome roles, inspect shape and influential points, preserve the sampling unit, and separate description, prediction, and causal estimation before interpreting coefficients.
Four scatterplots share a similar correlation but show a line, curve, clustered groups, and one influential point. A causal diagram then introduces a common cause affecting both variables.
Worked example
A strong correlation between two trending time series can appear even without a direct relationship. Removing trend, modeling time, or using a design-aware approach may change the association.
Assumptions that carry the result
Pearson and simple linear regression require suitable linearity and independence for classical inference, with residual conditions for standard errors. Rank methods retain assumptions and do not solve confounding.
Interpret the result without overreaching
A coefficient does not prove direction, mechanism, transportability, or intervention effect. Prediction accuracy in one sample does not establish causal validity or future performance.
- Reporting r without a scatterplot.
- Extrapolating a fitted line beyond observed support.
- Treating adjustment for a few variables as automatic causal identification.
Practical questions
Frequently asked questions
Does zero correlation mean no relationship?
No. Pearson correlation can be zero for strong nonlinear or subgroup relationships.
Can regression prove causation after adjustment?
No. Causal interpretation requires justified design and assumptions about confounding, selection, measurement, model form, and interference.
Is Spearman always robust?
It is rank-based and captures monotone association, but ties, dependence, influential ordering, and sampling design still matter.
Further reading
Authoritative sources
Use these primary and professional resources to check definitions, conventions, or requirements that may extend beyond this guide.