Are Variables Related? · 变量之间有关系吗？
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| statistical question/stəˈtɪstɪkl ˈkwestʃn/ | 统计问题 | tǒng jì wèn tí |
| association/əˌsəʊsɪˈeɪʃn/ | 关联 | guān lián |
| response variable/rɪˈspɒns ˈveərɪəbl/ | 响应变量 | xiǎng yìng biàn liàng |
| explanatory variable/ekˈsplænətəri ˈveərɪəbl/ | 解释变量 | jiě shì biàn liàng |
| variability/ˌveərɪəˈbɪlɪti/ | 变异性 | biàn yì xìng |
Do two things move together?
- Unit 1 looked at one variable at a time; now we ask how two variables relate.
- A statistical question 统计问题 about a relationship: "Do students who study more score higher?"
- We look for an association 关联 — a pattern where the two variables tend to move together.
- The whole unit is about finding, describing, and modeling these relationships.
两件事会一起变动吗？
- 第 1 单元一次只看一个变量；现在我们问两个变量之间有什么关系。
- 一个关于关系的统计问题：“学习时间更长的学生分数会更高吗？”
- 我们要找的是关联——两个变量倾向于一起变动的模式。
- 整个单元都是在寻找、描述并建模这些关系。
Explanatory and response
- The response variable 响应变量 is the outcome you want to explain or predict (the score).
- The explanatory variable 解释变量 is the one you think helps explain it (hours studied).
- Roughly: explanatory is the "input," response is the "output."
- By convention the explanatory variable goes on the $x$-axis, the response on the $y$-axis.
解释变量与响应变量
- 响应变量是你想解释或预测的结果（分数）。
- 解释变量是你认为有助于解释它的那个变量（学习时间）。
- 粗略地说：解释变量是“输入”，响应变量是“输出”。
- 按惯例，解释变量放在 $x$ 轴上，响应变量放在 $y$ 轴上。
Association, not proof
- An association just means the two variables vary together in some pattern.
- More studying tends to go with higher scores — that's an association.
- But association alone does not tell you one causes the other.
- Naming the association is the first step; explaining why comes much later.
是关联，不是证明
- 关联只是说明两个变量以某种模式一起变动。
- 学得越多往往伴随分数越高——这就是一种关联。
- 但仅有关联，并不能告诉你其中一个导致了另一个。
- 说清关联是第一步；解释为什么要等到很后面。
Why variability makes it tricky
- Real data are noisy — two people who study the same amount rarely score the same.
- This variability 变异性 blurs the pattern, so a weak relationship is hard to be sure about.
- An apparent link could be real, or it could be a fluke of this particular sample.
- Statistics gives us tools to judge whether a relationship is real or just chance.
为什么变异性让判断变难
- 真实数据是有噪声的——学习时间相同的两个人很少会得到相同的分数。
- 这种变异性模糊了模式，所以微弱的关系很难确定。
- 一个看似的联系可能是真的，也可能只是这一份样本里的巧合。
- 统计学给了我们工具，去判断一个关系是真实的还是仅仅出于偶然。
Deciding which variable is explanatory and which is response is a choice about the question, not something the data force on you. "Do taller people weigh more?" makes height explanatory; "do heavier people tend to be taller?" flips it. State your question first, then assign the roles — and remember that an association is not yet a cause.
判断哪个是解释变量、哪个是响应变量，是关于问题本身的选择，而不是数据强加给你的。“更高的人是否更重？”让身高成为解释变量；“更重的人是否往往更高？”则把角色对调。先说清你的问题，再分配角色——并且记住，关联还不是因果。
A study records each student's hours slept and their reaction time in a game.
- Explanatory: hours slept (the suspected cause). Response: reaction time (the outcome).
- Association: more sleep tends to go with faster reactions.
- But we can't yet say sleep causes faster reactions — other factors vary too.
一项研究记录了每个学生的睡眠时间和他们在游戏中的反应时间。
- **解释变量：**睡眠时间（怀疑的原因）。**响应变量：**反应时间（结果）。
- **关联：**睡得越多往往伴随反应越快。
- 但我们还不能说睡眠导致了更快的反应——还有其他因素也在变动。
A statistical question about two variables asks whether they are associated — whether they vary together. The explanatory variable ($x$) is used to explain or predict the response variable ($y$). Because of variability, an apparent association may be real or may be chance — that's what the rest of the unit sorts out.
一个关于两个变量的统计问题，问的是它们是否关联——是否一起变动。解释变量（$x$）用来解释或预测响应变量（$y$）。由于变异性，一个看似的关联可能是真的，也可能是偶然——这正是本单元其余部分要理清的。
An association between two variables · 两个变量之间的关联
Points drifting upward together — a positive association. · 点一起向上漂移——一种正关联。
In 'do students who study more score higher?', which is the response variable? · 在“学习更多的学生分数更高吗？”中，哪个是响应变量？
The score is the outcome we want to explain — the response. Hours studied is explanatory. · 分数是我们想解释的结果——即响应变量。学习时间是解释变量。
An observed association between two variables proves that one causes the other. · 两个变量之间观察到的关联，证明了其中一个导致了另一个。
Association is not causation — other explanations remain possible. · 关联不等于因果——其他解释仍然可能。
By convention, the explanatory variable is placed on the ___-axis. · 按惯例，解释变量放在 ___ 轴上。
Explanatory on x, response on y. · 解释变量在 x 轴，响应变量在 y 轴。
Why can an apparent relationship in one sample be uncertain? · 为什么一份样本中看似的关系会是不确定的？
Variability blurs patterns, so a weak apparent link may not be real. · 变异性模糊了模式，所以微弱的看似联系可能并不真实。
Which are true about explanatory and response variables? · 关于解释变量与响应变量，哪些是正确的？
Explanatory goes on the x-axis, not y — the rest are correct. · 解释变量放在 x 轴而非 y 轴——其余都正确。