Algebra
Data and statistics
Correlation
19 practice questions
2 video lessons
Theory + worked examples
Theory
Correlation describes how two variables move together:
- Positive: both increase together.
- Negative: one increases as the other decreases.
- None: no clear pattern.
Strength is how closely the points follow a line.
Positive, negative, and no correlation.
Describing correlation.
Direction and strength:
\[\text{direction: } \pm,\qquad \text{strength: tightness of the cluster}\]
Correlation is not causation.
How to describe correlation
- Look at the overall direction of the points.
- Rising: positive; falling: negative.
- Judge how tightly they cluster for strength.
- No pattern means no correlation.
Example 1 — Positive
Hours studied vs test score usually shows what correlation?
Solution
More study, higher score — positive.
Example 2 — Negative
Temperature vs hot-chocolate sales shows what correlation?
Solution
Warmer weather, fewer sales — negative.
Example 3 — Strength
What does a tight, near-linear cluster indicate?
Solution
A strong correlation.
Example 4 — No correlation
Shoe size vs test score usually shows what?
Solution
No correlation — unrelated variables.
Common pitfalls
Correlation does not imply causation.
Direction and strength are separate ideas.
Outliers can weaken apparent correlation.
Frequently asked questions
What is correlation?
How two variables move together — direction and strength.
What is positive correlation?
Both variables increase together.
What is negative correlation?
One increases as the other decreases.
Does correlation prove causation?
No.
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