Statistics / Unit 4: Two-Variable Data
4.2 Correlation
Notes
The correlation $r$ measures the direction and strength of a linear association.
- $-1 \le r \le 1$. The sign gives the direction. Values near $\pm 1$ mean a strong linear relationship and values near 0 mean a weak one.
- $r$ has no units and does not change if you change units (inches to centimeters) or swap $x$ and $y$.
- $r$ measures only linear association. A strong curved pattern can have $r$ near 0.
- Outliers can change $r$ a lot.
- Example: $r = -0.9$ is a strong negative linear association. $r = 0.4$ is a weak to moderate positive one.
Practice
Which correlation shows the strongest linear association?
Strength depends on distance from 0, so $|-0.92|$ is the largest.
Heights are converted from inches to centimeters. What happens to the correlation between height and weight?
Correlation has no units and is unaffected by changes of units.
A scatterplot shows a perfect U-shaped curve. The correlation is most likely:
The U-shape is strong but not linear, and $r$ measures only linear association.
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