# 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 `linearRegressionY` | | 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 linear regression Pass the observations directly to `linearRegressionY`. The mark owns the least-squares fit, semantic-domain samples, optional confidence band, and aggregate source lineage. Keep the dot layer separate so each observation remains independently focusable. Set `ci: 0` when only the fitted line is needed. The default `0.95` band uses a Student-t interval for the fitted mean. See the [linear regression mark](../reference/marks/regression.md) for grouping, sampling, and degenerate-fit behavior. The dot layer still preserves every observation while the regression mark owns only its derived model geometry. ## 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. ## Separate visible cells from nearest-point focus Voronoi cells make each point's nearest region visible. The optional `voronoi` mark paints those cells but deliberately adds no focus candidates. A layered `dot` mark remains the semantic source for pointer focus, keyboard navigation, and tooltips. See the [`voronoi` mark](../reference/marks/voronoi.md) for final-screen cell geometry and stable identity. [Tooltips and Focus](../guides/tooltips-and-focus.md) defines the focus and formatting model. Use a `ChartSpatialIndexFactory` when lookup performance matters but the cells should not be painted. ## 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](../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 lag pairs in data preparation. Keep lookup-only spatial indexes in interaction capabilities; use `voronoi` only when cells are part of the visible encoding. - 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).