Scatterplots
Introduced| English | Meaning |
|---|---|
| scatterplot/ˈskætəplɒt/ | A plot of paired data as points, showing form, direction, strength and outliers. |
| linear/ˈlɪnɪə/ | Describing a straight-line relationship or an expression whose variables appear only to the first power without products between them. |
Plotting two number variables
- When both variables are quantitative, show them in a scatterplot 散点图.
- Each individual is one point: explanatory value across ($x$), response value up ($y$).
- The cloud of points reveals whether — and how — the two variables move together.
- The scatterplot is the single most important graph in this unit.
Direction, form, strength
- Direction: positive (up together) or negative (one up, other down)?
- Form: roughly linear 线性 (a straight-line trend) or curved?
- Strength: how tightly do the points hug the pattern — tight, or a loose cloud?
- Describe all three, every time, in the context of the variables.
A line of best fit runs through the middle of the scattered points
Outliers and departures
- Look for outliers — points far from the overall pattern.
- Note clusters, gaps, or a bend where the form changes.
- An outlier in a scatterplot can be unusual in $x$, in $y$, or in the combination.
- Flag these departures; they often carry the most interesting information.
Describe in context
- Put it together: "As $x$ increases, $y$ tends to increase — a moderately strong, positive, linear association."
- Always name the real variables and their units, not just "$x$ and $y$."
- Mention any outlier or unusual feature explicitly.
- A complete description = direction + form + strength + unusual features, in context.
A scatterplot description needs all three of direction, form, and strength — plus any outliers. Skipping "form" is the common slip: if the trend actually curves, saying "strong positive" without noting the curve misleads, because a straight-line summary (and the correlation $r$) won't fit a bent pattern.
Hours studied ($x$) vs. exam score ($y$) for a class.
- Direction: positive — more study, higher score.
- Form & strength: roughly linear, moderately strong (points cluster near a line).
- Unusual: one student studied many hours but scored low — an outlier worth investigating.
A scatterplot plots two quantitative variables (explanatory on $x$, response on $y$). Describe its direction (positive/negative), form (linear/curved), and strength (tight/loose), and note any outliers — always in context with the real variables.
Write from a point off the pattern
- Most points on a scatterplot follow a straight upward pattern.
- One point sits far above that pattern.
What is that far point called?
An outlier departs from the overall pattern.
What is the point far above the line?
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It does not follow the rest of the points.
A scatterplot with a linear trend
Drag to see how direction and strength change the cloud of points.
A complete scatterplot description mentions which features?
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All four — direction, form, strength, and any outliers, in context.
Points go up to the right: as x increases, y increases. The direction is...
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Up together = positive direction.
On a scatterplot, the explanatory variable goes on the horizontal (x) axis.
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Explanatory on x, response on y.
A point far from the overall pattern of a scatterplot is called an ___.
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Outliers are departures from the overall pattern.
If the points hug a straight line very tightly, the association is...
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Tight clustering around the pattern = strong.