Correlation Demonstrator
Change the underlying relationship, drag individual observations and see how Pearson correlation, R² and the least-squares line respond in real time.
Correlation is a summary of a linear pattern—not a substitute for looking at the data.
This demonstrator combines direct controls with draggable scatter-plot observations. Learners can change direction, noise, range, sample size, curvature and an influential point, then immediately observe Pearson r, R² and the regression line.
Correlation Demonstrator — Step by Step
Eight locked stages move from a baseline relationship through direct manipulation, draggable observations, leverage, range restriction, nonlinearity, a challenge and management interpretation.
Scatter Pattern, Pearson r and Regression Fit
Reveal the correlation context to begin.
Interpret the coefficient in context.
Build Your Own Correlation Scenario
Experiment Mode is isolated from the guided demonstration. Adjust the relationship controls and drag observations without changing guided progress.
Test correlation interpretation.
Correlation interpretation cues
Direction
Positive r means higher x tends to occur with higher y. Negative r means higher x tends to occur with lower y.
Strength
The magnitude |r| describes linear tightness. Values near 1 are stronger; values near 0 are weaker linearly.
R²
For simple linear regression, R² = r². It summarises the proportion of variance explained by the fitted straight line.
Leverage
Points far from the centre of the x-values can exert disproportionate influence on r and the fitted line.
Nonlinearity
A small Pearson r does not imply no relationship. Inspect the scatter plot for curved or segmented patterns.
Causation
Correlation alone does not establish cause. Consider design, timing, confounding variables and alternative explanations.
Pearson r is useful only when its linear pattern, leverage, range, nonlinearity and causal limitations are understood.