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Learning outcomes

  • define correlation
  • interpret the sign and magnitude of correlation
  • distinguish weak and strong linear association
  • avoid common correlation misconceptions

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What is correlation?

  • Correlation measures the strength and direction of linear association between two numerical variables.
  • It is usually represented by r.

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Range of correlation

  • -1 <= r <= 1
Interpretation:
  • r near 1 -> strong positive linear association
  • r near -1 -> strong negative linear association
  • r near 0 -> weak or no linear association

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Important cautions

  • Correlation describes linear association.
  • A curved relationship may have low correlation even when variables are related.
  • Correlation does not imply causation.

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Reading values conceptually

  • 0.85 -> strong positive
  • -0.72 -> strong negative
  • 0.10 -> weak linear association

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Exam hints and traps

  • Sign shows direction, magnitude shows strength.
  • -0.9 is stronger than 0.4 because strength uses absolute value.
  • Zero correlation does not mean no relationship of any kind.
  • High correlation is not proof of cause-effect.

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Quick practice

  1. Which is stronger: r = -0.8 or r = 0.5?
  2. What does the sign of r show?
  3. Can correlation prove causation?

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Answer key

  1. -0.8
  2. Direction of linear association
  3. No