Scatter Plots

Scatter plots display paired numerical data and reveal direction, form, strength, clusters, outliers, and possible associations.

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A trend line summarizes association, not automatic causation. A scatter plot contains a fitted line and visible residual segments. The points cluster around the trend while a caption cue distinguishes correlation from a causal claim.

A scatter plot places each paired numerical observation $(x,y)$ as one point to study how two variables vary together.

Paired data

Each point must join measurements from the same individual, object, place, or time. A student’s study time and test score form a pair; sorting each column separately would destroy those relationships.

Choose the explanatory variable for the horizontal axis and response variable for the vertical axis when that distinction makes sense. Label both axes with units and use scales that show the data honestly.

Direction

A positive association means larger $x$-values tend to accompany larger $y$-values. A negative association means larger $x$ tends to accompany smaller $y$. No association means no clear directional pattern.

Direction describes a tendency, not a rule that every point must follow.

Form and strength

Form may be linear, curved, clustered, or more complicated. Strength describes how tightly points follow that form. A strong curved association can have weak linear correlation if the wrong summary is used.

Describe a plot with direction, form, strength, and unusual features rather than saying only “there is correlation.”

Outliers and influential points

An outlier lies away from the main pattern. Check for data-entry error, unusual context, or a legitimate exceptional case. An influential point is one whose removal substantially changes a fitted model; it may be far in the $x$-direction even if it follows the trend.

Do not delete points merely to improve a line. Document and justify any exclusion.

Common mistakes

Connecting points in arbitrary order. A scatter plot is not automatically a time-series line graph.

Claiming causation from association. Consider study design and other variables.

Ignoring axis scale. Truncated or uneven scales can exaggerate patterns.

Extrapolating far beyond the data. The fitted relationship may not continue.

Quick self-check

Are observations correctly paired?
What are direction, form, strength, and unusual features?
Is a linear model appropriate?
Is my prediction interpolation or extrapolation?
Am I distinguishing association from causation?