SAME FIT
Same fitted summary. Different structure.
Tap a point or choose its table row. Row numbers are table positions, not shared subjects across datasets.
Same eleven points · actual fitted line
Read the study
Four sets of eleven points. Their familiar summaries agree when rounded. Put the pictures beside one another, then look at what each fitted line leaves behind.
What stays the same
This is Anscombe’s quartet: four fixed datasets, each with eleven observations. The stated means, sample variances, correlation and fitted coefficients agree at the explicitly displayed rounding precision. The page checks that agreement from the data.
Every panel uses x from 0 to 20. Point view uses y from 0 to 15; residual view uses y − ŷ from −4 to 4. Scales are fixed within each view and shared by all four datasets. Switching views changes the vertical quantity and its labeled scale.
What a residual measures
ŷ = a + bx
residual = y − ŷ
The line minimizes the sum of squared vertical residuals, with an intercept. It is fitted separately to each dataset using its full-precision computed coefficients. A small residual says that a point is near this fitted line; it does not measure how strongly that point determines the fit.
In IV the isolated point at x = 19 lies on the fitted line, yet provides all the separation in x from the other ten observations. A residual alone would miss that role.
What this specimen establishes
These nearly matching numerical portraits coexist with visibly different structures. That is a reason to inspect the observations and residuals alongside the summary, not a claim that every fitted relationship is misleading.
The page compares a finite published quartet. It does not rank the datasets, infer a data-generating process, or diagnose every regression with one pattern. Linked row selection follows table position only; the four rows are not observations of the same entity.
Source and arithmetic
F. J. Anscombe, Graphs in Statistical Analysis (1973), The American Statistician 27(1), 17–21. Original paper.
The numbers are transcribed from R’s dataset source. R’s documentation includes a comparison of the fitted coefficients.
Means, centered sums, sample variances, Pearson correlation and ordinary least squares are recomputed locally. Six-place audit values use browser floating-point arithmetic. No solver, random sampling, or data morph is involved.
A shared numerical portrait.
Rounded agreement, not exact equality.
OLS line at 2 decimal places: —. Variances use n − 1. Audit the rounding ↓
Inspect the four datasets together
Shared axes · x: 0–20 · y: 0–15
Variation around a rising line.
A clear bend remains in the residuals.
One point sits above the otherwise narrow trend.
Ten points share x = 8. One point sets the span.
Solid lines are each dataset’s actual least-squares fit. The selected point has a larger outline; its vertical segment is y minus fitted y.
The line is a summary.
It carries a slope and an intercept. It does not carry the curve in II, the unusual point in III, or the concentration at a single x in IV. The residual view makes those differences easier to inspect.
The numbers agree at a stated resolution.
The structures remain different.
Inspect a consequential row.
These buttons highlight existing observations. No points are removed, moved, or replaced; the fit and its summary continue to use all eleven.
Audit the numbers · actual fits and rounding
Every value below is recomputed from the displayed observations. Six decimal places expose differences hidden in the summary above; they are still a decimal display, not an assertion of exact equality. Scroll the table sideways on smaller screens to compare all four.
| Statistic | I | II | III | IV | Max − min | Summary |
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Sample variance y is shown to 1 decimal place in the shared summary: at 2 places, III and IV give 4.12 while I and II give 4.13. The other displayed summary statistics use 2 places. The actual fitted lines and residuals always use the computed coefficients, before rounding.
Inspect the source observations
| Row | I · x, y | II · x, y | III · x, y | IV · x, y |
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