Integrated Math 1 / Unit 7: Descriptive Statistics
7.6 Correlation and Causation
Notes
The correlation coefficient $r$ is between $-1$ and $1$. It measures the strength and direction of a linear relationship.
- $r$ near 1: strong positive. $r$ near $-1$: strong negative. $r$ near 0: little or no linear relationship.
- The sign gives direction; the distance from 0 gives strength.
- Correlation does not imply causation: a lurking variable may cause both.
- Example: ice cream sales and sunburns are both higher in summer; ice cream does not cause sunburn.
Practice
What does $r = -0.92$ tell you about a scatter plot?
The value is close to $-1$, so the relationship is strong and negative.
A town finds that months with more ice cream sales also have more swimming accidents. What is the best conclusion?
Correlation does not prove causation; hot weather is a likely lurking variable.
Which correlation coefficient shows the strongest linear relationship?
Strength depends on how close $|r|$ is to 1, and $0.95$ is the closest.
Ready for more? Take the Unit 7 test.