Scatterplots · 散点图
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| scatterplot/ˈskætəplɒt/ | 散点图 | sàn diǎn tú |
| linear/ˈlɪnɪə/ | 线性 | xiàn xìng |
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.
画出两个数值变量
- 当两个变量都是数值型时，用散点图来展示。
- 每个个体是一个点：解释变量的值向右（$x$），响应变量的值向上（$y$）。
- 这团点揭示了两个变量是否——以及如何——一起变动。
- 散点图是本单元里最重要的一张图。
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.
方向、形状、强度
- 方向：**正（一起上升）还是负**（一个升、另一个降）？
- 形状：大致是线性的（直线趋势）还是弯曲的？
- **强度：**这些点贴合模式有多紧——很紧，还是松散的一团？
- 每次都要结合变量的语境，描述这三点。
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.
离群值与偏离
- 寻找离群值——远离整体模式的点。
- 留意群、间隙，或形状发生变化的拐弯处。
- 散点图中的离群值可能在 $x$ 上异常、在 $y$ 上异常，或在两者的组合上异常。
- 标出这些偏离；它们往往携带着最有意思的信息。
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.
结合语境描述
- 把它拼起来：“随着 $x$ 增加，$y$ 往往增加——一种中等偏强的、正的、线性的关联。”
- 总要点出真实变量及其单位，而不只是“$x$ 和 $y$”。
- 明确提到任何离群值或异常特征。
- 完整的描述 = 方向 + 形状 + 强度 + 异常特征，且结合语境。
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.
描述散点图需要方向、形状、强度三者齐全——外加任何离群值。漏掉“形状”是常见的疏忽：如果趋势其实是弯曲的，只说“强正”而不提弯曲会产生误导，因为直线概括（以及相关系数 $r$）无法拟合一个弯曲的模式。
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.
一个班的学习时间（$x$）对考试分数（$y$）。
- **方向：**正——学得越多，分数越高。
- **形状与强度：**大致线性、中等偏强（点聚集在一条线附近）。
- 异常：有一个学生学了很多小时却得分很低——一个值得调查的离群值。
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.
散点图画出两个数值变量（解释变量在 $x$，响应变量在 $y$）。描述它的方向（正/负）、形状（线性/弯曲）和强度（紧/松），并标出任何离群值——始终结合真实变量的语境。
A scatterplot with a linear trend · 带线性趋势的散点图
Drag to see how direction and strength change the cloud of points. · 拖动以观察方向和强度如何改变这团点。
A complete scatterplot description mentions which features? · 完整的散点图描述会提到哪些特征？
All four — direction, form, strength, and any outliers, in context. · 四者全部——方向、形状、强度和任何离群值，结合语境。
Points go up to the right: as x increases, y increases. The direction is... · 点向右上方走：x 增加时 y 增加。方向是……
Up together = positive direction. · 一起上升 = 正方向。
On a scatterplot, the explanatory variable goes on the horizontal (x) axis. · 在散点图上，解释变量放在水平（x）轴上。
Explanatory on x, response on y. · 解释变量在 x 轴，响应变量在 y 轴。
A point far from the overall pattern of a scatterplot is called an ___. · 远离散点图整体模式的点叫做 ___。
Outliers are departures from the overall pattern. · 离群值是对整体模式的偏离。
If the points hug a straight line very tightly, the association is... · 如果点非常紧地贴合一条直线，则关联是……
Tight clustering around the pattern = strong. · 紧密聚集在模式周围 = 强。