散布図、相関、慎重な予測 · 上級者向け
導入済み| English | 意味 |
|---|---|
| correlation/ˌkɒrɪˈleɪʃn/ | 相関 |
Taller students may tend to have larger shoes. A plotted association does not prove that changing someone’s height would directly change their shoe size.
- Taller students may tend to have larger shoes. A plotted association does not prove that changing someone’s height would directly change their shoe size.
- This lesson studies correlation 相关性: A pattern of association between two measured variables.
Choose the mathematical structure
- Plot paired observations as points, with one variable on each axis. Positive correlation rises, negative falls and no correlation has no clear trend. Strong/weak describes how tightly points follow a trend, not its steepness. Draw an estimated line of best fit through the middle of the pattern, balancing points around it; it need not pass through the origin. Interpolation stays within observed inputs; extrapolation goes outside them.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
直線 y=40+4.5x は 1-5 時間の学習に対する得点を表す。なぜ x=10 における予測は信頼できないか？
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
1-5 の範囲内では、直線は観測点間の補間である。x=10 において、利益が直線的に継続するという仮定は検証されていない。向上は通常頭打ちになるため、85 は測定ではなく推測である。
Work through a checked case
- Check the result against the starting quantities. Substitute into the original relation, or compare the graph and numerical answer where appropriate.
Observed study hours 1,2,3,4,5 with scores 44,49,53,58,61 show a positive trend. An estimated line y=40+4.5x predicts 53.5 at x=3 and 56.2 at x=3.6. These inputs are inside 1–5, so the predictions interpolate. At x=10 the line gives 85, but this extrapolation may fail if gains flatten or the group differs. Sleep hours and tiredness may show a negative correlation; an almost horizontal cloud with no ordered pattern may show little correlation. A shared cause such as prior preparation can affect both study time and score; the plot alone does not establish causation.
散布図、相関、慎重な予測
ペアの観測点をプロットし、各軸に1つの変数を配置する。
例題の命題を分類し、それぞれの判断を正当化する単位または不変量を説明せよ。
y=40+4.5x という近似式を用いて、x=3 における y の値を予測せよ。
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
40+4.5×3=53.5.
Test a tempting shortcut
- Do not join scatter points in observation order as though they formed a time series. A steep line need not imply strong correlation. An extrapolated formula value is a prediction whose assumptions need scrutiny.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
A positive correlation proves that one variable causes the other. This claim is false. Explain which definition or assumption it violates.
x=10 における予測を行う。
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
40+4.5×10=85、外挿のリスクを含む。
正の相関は、ある変数が他の変数を引き起こすことを証明するものではない。
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
観測順に散点図のプロットを結んで時間系列のように扱わないでください。傾きの大きい直線が強い相関を意味するとは限りません。外挿された数値は、その仮定を検証すべき予測です。
Interpret a new situation
- AQA S6 Foundation includes correlation, estimated best-fit lines, predictions and dangers of extrapolation. State the observed input range, association direction/strength and the limits of a causal claim.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
観測された x の範囲 1–5 の幅を求める。
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
5-1=4; x=10 での予測は範囲外にある。
散布図の各用語とその意味を対応させよ。
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
相関の強さはトレンド周围的の密集度に関するものであり、急峻さではない。また、関連性だけでは因果関係を証明しない。
Use this in your course
- 8300 · Higher · 3.6. Match the target tier and specification before assigning extensions.
- Give the method before the final answer, and use the paper's calculator and formula rules. Review a wrong answer by locating the first invalid step.
A pattern of association between two measured variables. Choose the relationship, show the method, check its assumptions and interpret the result.