Research Guide

Correlation vs Regression

The difference between measuring a linear association (correlation) and modelling a relationship to make predictions (regression), and how R² connects them.

Correlation and regression both describe relationships between variables, but they answer different questions. Correlation measures the strength and direction of a linear association. Regression models the relationship so you can predict one variable from another.

The two are closely related — the correlation coefficient is the foundation of simple linear regression — but treating them as interchangeable leads to confusion about what a number means.

What correlation measures

The Pearson correlation coefficient r ranges from −1 to +1. The sign tells you the direction of the relationship and the magnitude tells you how tightly the points cluster around a straight line. It is symmetric: r between X and Y is the same as r between Y and X, and it is unitless, so it does not depend on the scales of the variables.

Correlation measures only linear association. Two variables can have a strong curved relationship and a correlation near zero.

What regression does

Simple linear regression fits the line y = b0 + b1·x that best predicts the outcome y from the predictor x, using the least-squares criterion (minimising the sum of squared vertical distances). The slope b1 is the expected change in y for a one-unit change in x. Regression is asymmetric: it treats x as the predictor and y as the outcome, so swapping them gives a different line.

The PanelRoster regression calculator fits this line and reports the slope, intercept and R² from your paired data.

How R² connects them

For simple linear regression, R² (the coefficient of determination) equals the square of the correlation coefficient, r². It is the proportion of the variance in the outcome explained by the predictor. An r of 0.6 means R² = 0.36 — the predictor explains 36% of the variation in the outcome. R² between 0 and 1 is a useful summary of fit, but a high R² alone does not prove the model is useful or correct.

Correlation is not causation

Neither correlation nor regression establishes cause and effect. A strong association can arise from a common cause, reverse causation, or pure coincidence. Establishing causality requires a design that controls for confounding — most convincingly, random assignment. Always interpret relationships in the context of the study design.

Key takeaways

Correlation (r) summarises the strength and direction of a linear association; it is symmetric and unitless.
Regression models a predictor→outcome relationship so you can make predictions.
In simple regression, R² = r²: the share of outcome variance explained by the predictor.
Neither implies causation.

Tools used in this guide

References

References are provided for further reading; PanelRoster is not affiliated with the linked resources.