| English | 의미 |
|---|---|
| regression line/rɪˈɡreʃn laɪn/ | 회귀직선 |
| extrapolation/ekˈstræpəleɪʃn/ | 외추 |
A line through the cloud
- When a scatterplot looks linear, summarize it with a regression line 回归线.
- We write the predicted response as $\hat{y} = a + bx$ (the hat means "predicted").
- $a$ is the $y$-intercept, $b$ is the slope — the line's recipe.
- The line lets us predict $y$ from any $x$ and describe the trend precisely.
Reading the slope
- The slope $b$ is the predicted change in $y$ for each $1$-unit increase in $x$.
- In context: "each extra hour of study predicts about $b$ more points."
- Its sign matches the direction of the association (positive or negative).
- The slope is where almost all the interpretation credit lives on the exam.
Reading the intercept
- The intercept $a$ is the predicted $y$ when $x = 0$.
- Sometimes meaningful ("baseline score with zero study"), sometimes not.
- If $x = 0$ is far outside the data, the intercept is just a mathematical anchor.
- Interpret it in context — and be honest when $x=0$ makes no real sense.
Don't extrapolate
- Use the line only within the range of the observed $x$ values.
- Extrapolation 外推 — predicting far beyond the data — is unreliable.
- The linear pattern may simply not continue out there.
- A model that fits students studying $0$–$8$ hours says nothing trustworthy about $40$ hours.
Interpret the slope as a predicted change, not an actual one: "each extra hour is associated with about $b$ more points," not "causes." And never trust a prediction from extrapolation — plugging in an $x$ far outside the data range gives a number the data can't support, even if the arithmetic works.
For study hours, $\hat{y} = 55 + 4x$ (score predicted from hours).
- Slope $4$: each extra hour of study predicts about $4$ more points.
- Intercept $55$: a student who studies $0$ hours is predicted to score $55$.
- Predict at $x=3$: $\hat{y} = 55 + 4(3) = 67$ points — safely inside the data range.
A least-squares regression line $\hat{y} = a + bx$ models a linear trend. The slope $b$ is the predicted change in $y$ per $1$-unit increase in $x$; the intercept $a$ is the predicted $y$ at $x=0$. Predict only within the data range — extrapolation beyond it is unreliable.
최소제곱직선
fitting된 선은 데이터 내의 모든 x에 대해 y를 예측합니다.
y-hat = 55 + 4x일 때, x = 3시간일 때 점수를 예측하십시오.
난이도 2/5 · 140 코인 + 오늘 첫 완료 시 소액 보너스
55 + 4(3) = 55 + 12 = 67.
y-hat = 55 + 4x에서 기울기 4는 무엇을 의미합니까?
난이도 1/5 · 100 코인 + 오늘 첫 완료 시 소액 보너스
기울기 = x가 1단위 증가할 때 y의 예측 변화량.
관측된 x 범위를 훨씬 벗어난 곳에 모델을 사용하여 예측하는 것을 외삽(extrapolation)이라 하며, 이는 신뢰할 수 없습니다.
난이도 1/5 · 100 코인 + 오늘 첫 완료 시 소액 보너스
외삽은 위험합니다 — 패턴이 계속되지 않을 수 있기 때문입니다.
y-hat = a + bx에서 문자 a는 y-___입니다.
난이도 1/5 · 100 코인 + 오늘 첫 완료 시 소액 보너스
a는 y절편입니다: x = 0일 때의 예측 y값.
회귀 방정식에서 반응 변수를 예측하기 위한 단계 순서를 나열하십시오.
난이도 3/5 · 200 코인 + 오늘 첫 완료 시 소액 보너스
먼저 외삽을 방지하고, 이후 계산 및 해석을 수행