Scatter diagrams and correlation

Do tall people have bigger feet?

• Plot height against shoe size for 30 people and you'll see a pattern: taller people tend to have larger feet.
• A scatter diagram 散点图 reveals whether two variables are linked — and how strongly.

Correlation 相关性

• Positive correlation 正相关: as one goes up, the other goes up (points slope upward).
• Negative correlation 负相关: as one goes up, the other goes down (points slope downward).
• Zero correlation: no clear pattern (points scattered randomly).

A line of best fit 最佳拟合线 is one straight line through the middle of the points, with about as many on each side; use it to predict

Line of best fit

• If there is correlation, draw one straight line through the middle of the points, with roughly equal numbers on each side.
• Use it to predict values.

Positive correlation: both rise together. Negative: one rises as the other falls. Zero: no clear link

Outliers 异常值 on scatter diagrams

• A point far from the general pattern is an outlier.
• Investigate before removing it — it might be a genuine unusual case, or a recording error.

Scatter diagrams reveal patterns: positive (like a rising line), negative (like a falling line), or zero (no pattern).

Plot pairs and read an estimate

• Mark each pair with a small cross, not joined points. For $(1,12),(2,15),(3,19),(4,20),(5,24)$, a sensible by-eye line is close to $y=3x+9$; it spans all the data and roughly balances the points above and below.
• At $x=3.5$, this line estimates $y=19.5$. A nearby balanced line may give a slightly different answer. Predicting at $x=20$ is extrapolation and much less secure; correlation alone does not prove cause.

You've got it

Write from an estimate of 13

• Use the line y equals 2x plus 5.
• Estimate y at x equals 4.