Output: 1.0

This indicates a perfect positive linear relationship for this small example.

🔹 18. Common Mistakes

• Thinking correlation must be between 0 and 1 → Correlation can be negative: -1 <= r <= 1

• Thinking r = 0 means absolutely no relationship → It means there is no linear relationship detected by Pearson correlation. A nonlinear relationship may still exist.

• Assuming high correlation proves causation → Correlation only tells us that variables move together. It does not establish cause and effect.

🎯 Key Takeaways

• Covariance measures how two variables change together.

• Positive covariance indicates that variables tend to move in the same direction.

• Negative covariance indicates that they tend to move in opposite directions.

• Correlation measures the direction and strength of a linear relationship.

• Pearson correlation ranges from -1 to +1.

• Correlation is unitless and easier to interpret than covariance.

• A correlation of +1 indicates perfect positive linear association.

• A correlation of -1 indicates perfect negative linear association.

• A correlation of 0 indicates no linear association.

• Correlation does not imply causation.

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