# Scatterplots and Relationships
Scatterplots answer how two quantitative measures vary together. Position
carries the primary evidence. Color, radius, a fitted line, or chronological
connections should add one clearly stated dimension rather than compete with
that relationship.
## Choose the comparison
| Reader question | Start with |
| --------------------------------------------------------------- | ------------------------------------------- |
| Do two quantitative measures move together? | A scatterplot |
| What linear tendency summarizes that relationship? | Scatterplot plus a prepared regression line |
| How does the relationship evolve in a known order? | A connected scatterplot |
| Does a series depend on its previous observation? | A lag plot |
| Which dense point is closest to the pointer or keyboard cursor? | A scatterplot with a spatial focus strategy |
Do not infer causation from proximity or a fitted trend. Show the model and
preparation only when they answer the stated question.
## Add a prepared regression
A fitted line is derived data. Calculate its coefficients in the application,
then render the raw observations and fitted endpoints as independent layers.
This separation lets the dot layer preserve every observation while the line
layer consumes only the model output. See
[Marks and Layering](../concepts/marks-and-layering.md) for composition and
[Scales and D3](../concepts/scales-and-d3.md) for the application-owned
statistics boundary.
## Connect observations only when order matters
A connected scatterplot turns sequence into a path through two-dimensional
measure space. Chronological labels and direction arrows make that additional
ordering visible.
Without an explicit order, connecting points invents a relationship. Keep the
path, arrow, selected labels, and points as separate layers so each can use the
same scales without sharing renderer-specific state.
## Compare each observation with its predecessor
A lag plot moves time out of the axis and into data preparation. Each point
pairs a current value with the previous value; an identity rule shows where
those values would be equal.
Make the lag length explicit and decide how the first observation is handled.
The chart should receive the resulting pairs rather than conceal the shift
inside a mark.
## Use spatial focus for dense points
Nearest-point interaction should use two-dimensional distance when both axes
matter. A spatial index can make that lookup efficient without changing the
dot grammar or storing tooltip state inside the mark.
[Tooltips and Focus](../guides/tooltips-and-focus.md) defines the focus and
formatting model. Use [Interactions and Selections](../guides/interactions-and-selections.md)
when focused data also changes application state.
## Production checks
- Use quantitative scales with intentional domains on both axes. Use a
logarithmic scale only when multiplicative distance is the intended reading;
see [Scales and D3](../concepts/scales-and-d3.md).
- Map magnitude through an area-preserving radial scale when point size carries
a third quantitative value.
- Control opacity or aggregate spatially before thousands of overlapping dots
obscure the distribution. See [Large Data](../guides/large-data.md).
- Keep regression, lag pairs, and spatial indexes in data preparation or
interaction capabilities rather than the dot mark.
- Provide keyboard-equivalent focus and a textual value path, as described in
[Accessibility](../guides/accessibility.md).
The channel and styling contracts for points are in
[Dot and Hexagon Marks](../reference/marks/dot-and-hexagon.md).