Anscombe’s Quartet, explained.
Anscombe’s quartet comprises four datasets with nearly identical summary statistics but markedly different graphical structures.
Why it happens
The original rounded coordinates are plotted with least-squares slope and correlation. Removing a point recomputes both. In the fourth dataset, removing the sole non-eight x value makes slope and correlation undefined.
Anscombe’s quartet comprises four datasets with nearly identical summary statistics but markedly different graphical structures.
Read the result
Plot shape and point influence matter even when rounded slopes and correlations look nearly identical.
A worked example
Four regressions with matching summaries
Switch among the four original rounded datasets and compare their least-squares summaries.
Inspect curvature, an unusual response and the leverage point rather than relying on a correlation alone.
In dataset four omit the largest-x point; all remaining x values equal eight, making slope and correlation undefined.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
The original rounded coordinates are plotted with least-squares slope and correlation. Removing a point recomputes both. In the fourth dataset, removing the sole non-eight x value makes slope and correlation undefined.
Where this idea is useful
A practical use
Inspect raw plots, outliers and model shape before treating a regression summary as a sufficient description.
A common misconception
“The same correlation means the same relationship.”
A summary can conceal nonlinearity, leverage and outliers. Similar correlation coefficients do not establish interchangeable data structures.
What this explanation leaves out
- Coordinates are rounded original values. A descriptive fit does not establish a causal or predictive model, and some omissions make a slope undefined.
Why does removing a point sometimes remove the slope entirely?
Least-squares slope divides by variation in x. With no variation in x, the denominator is zero and a finite slope is unidentified.
What would you plot before trusting the next numerical summary you receive?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.