Common mistake 1 with Scatter plot

Reading causation off a slope. The chart contains no controls whatsoever.

Common mistake 2 with Scatter plot

Fitting a line to two clusters and interpreting it. The line is describing the gap between the clusters, not a relationship within either.

Common mistake 3 with Scatter plot

Ignoring that both variables have error. The fitted line here is y on x, and regressing x on y gives a different line through the same cloud.

Common mistake 4 with Scatter plot

Adding a smoother and reading its wiggles. A flexible smoother will always find structure at the ends of the range, where it has fewest points to constrain it.

EconStatsCraft › Scatter plot

Scatter plot

The chart for "do these two move together". Turn the fitted line on and it reports the slope and the correlation, which are the two numbers a scatter is usually being read for.

What it needs

Horizontal variable
Vertical variable

The intuition

A scatter plot is the most information-dense chart in common use: two variables, one point per observation, nothing aggregated away. It is the right first look at any pair of continuous variables, and it is the only common chart where the reader can see the things summary statistics hide - clusters, curvature, outliers, and the fact that a correlation of 0.8 can come from several completely different pictures.

When to use it

Before any regression of one variable on another, always. And afterwards, to check the relationship you fitted is the relationship in the data.

Where the estimator comes from

Each observation is a point at (x_i,y_i): position on two aligned scales, which is the single most accurately judged visual encoding. No aggregation happens, so the display shows the joint distribution rather than a summary of it. A fitted line added on top is a MODEL, not data, and the distinction matters - Anscombe's quartet is four datasets with identical means, variances, correlation and regression line, and four completely different scatter plots.

What it assumes

Both axes are numeric and on a meaningful scale. A category on the x axis wants bars.
The points are comparable observations. Pooling two populations produces a cloud whose slope belongs to neither - this is Simpson's paradox as a picture, and the "Split by" option is how you check for it.
The points are independent. Repeated measurements of the same unit look like extra evidence and are not, and a scatter cannot show you that they are repeats.
Overplotting has been considered. With thousands of points the dense region is a solid mass whose shape says nothing about how many observations are in it.

Statistical properties

Overplotting hides density. With a few thousand points the middle of the cloud saturates and a region containing ten points looks the same as one containing ten thousand. Transparency, hexbinning or a small point size are the fixes.
A fitted line is a claim about the data, not part of it. Draw it, but the points must remain visible or the chart has become a line chart with decoration.
The aspect ratio changes the apparent slope. Cleveland's banking to 45 degrees - choosing the ratio so the average line segment sits near 45 degrees - is the principled choice.
Correlation is not the picture. Anscombe's quartet and the Datasaurus dozen both make the point: identical summary statistics, wildly different scatters, and only the plot distinguishes them.
A scatter shows association and nothing about direction. Which variable goes on which axis is a claim about what explains what, and it is a claim the chart cannot support.
Rounded or discretised data forms visible lattices. That is a property of the recording, not of the relationship, and jittering makes it readable at the cost of showing values that were not measured.

How to read the output

Look for curvature before reading the slope. A straight line through a curve has a slope, and it means nothing.
Look for the one or two points at the edge. Remove them mentally: if the line would move a lot, the result is about those points and not about the sample.
r near zero does not mean unrelated, it means not LINEARLY related. A U shape can have r of exactly zero.
With many thousands of points the cloud saturates and structure disappears. A heat map or a density plot recovers it.
Look at the margins as well as the cloud. A skewed marginal distribution on either axis explains more apparent curvature in the relationship than most transformations do.
The fitted line is a summary of the conditional mean, not a description of the individual points. A high correlation with a wide scatter still means individual prediction is poor.

A worked reading

Anscombe's four datasets share a mean of 9 in x and 7.5 in y, the same variances, a correlation of 0.816 and the same fitted line y = 3 + 0.5x. Plotted, one is a clean linear relationship, one is a perfect parabola, one is a straight line with a single outlier dragging it, and one is a vertical stack of points at a single x with one point far to the right doing all the work. Four identical summary tables, four incompatible stories. This is the entire argument for plotting before modelling, and it takes one chart to make.

Symptom → diagnosis → what to do

If you see this	It means	Do this
A solid blob in the middle	Overplotting	Reduce opacity, shrink points, or hexbin
Points in a grid pattern	Values rounded at collection	Jitter, and say that you did
A strong line and a low R-squared	A few outliers dominating	Check the residuals; consider a robust fit
The relationship looking flat	Aspect ratio, or an axis with an outlier stretching it	Bank to 45 degrees; check the range
Two visible clouds	A hidden grouping variable	Colour by the candidate group and see
Curvature	A linear fit is the wrong model	The scatter is telling you something the correlation cannot

Common mistakes

Reading causation off a slope. The chart contains no controls whatsoever.
Fitting a line to two clusters and interpreting it. The line is describing the gap between the clusters, not a relationship within either.
Ignoring that both variables have error. The fitted line here is y on x, and regressing x on y gives a different line through the same cloud.
Adding a smoother and reading its wiggles. A flexible smoother will always find structure at the ends of the range, where it has fewest points to constrain it.

Where to read this properly

Anscombe (1973), "Graphs in Statistical Analysis", The American Statistician 27(1).
Matejka and Fitzmaurice (2017), "Same Stats, Different Graphs", CHI - the Datasaurus.
Cleveland, Visualizing Data (1993), on banking to 45 degrees.

All analyses

Data & variables

Each example is simulated from a known model, so you can check whether the estimator recovers the truth - and nothing here is anyone's private data.

Filter variables

Drag a variable into a slot on the right - or just click it.

Choose an example dataset above to begin.

Choose a transformation - it opens in the data editor, with a live preview.

Apply to

Multiply by

Columns ctrl-click for several

Group by ctrl-click for several

Within groups

Statistic

Bands

How many

Cut points

Keep rows where

Value

and

Fill with

Value

Also mark which rows were filled

Rules

Base period = 100

Which part

Percent at each tail

Threshold

Survey weight optional

Direction

Names column

Values column

Largest first

Delete them, not just count them

Read this column as

Tidy the text

New name optional

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Scatter plot

What it needs

The intuition

When to use it

Where the estimator comes from

What it assumes

Statistical properties

How to read the output

A worked reading

Symptom → diagnosis → what to do

Common mistakes

Where to read this properly

See also

Related Charts

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