Correlation

The correlation coefficient r (from −1 to 1) measures how close the points are to a straight line: near 1 strong positive, near −1 strong negative, near 0 none. Correlation does not mean causation.

rCorrelation

📐 Formula

r = Σ(x − x̄)(y − ȳ) / √(Σ(x − x̄)² Σ(y − ȳ)²)

✏️ Worked example

Trend −1 with small noise: r ≈ −0.95, a strong negative correlation. Increase the noise and r moves towards 0.

🌍 Where it is used

Testing relationships in science, economics and health data.

❓ Quick check

r = 0.02 means…

🏋️ Practice

EasyWhat r means a perfect falling line?

Answer: −1

MediumIce-cream sales and drownings correlate. Does ice-cream cause drowning?

Answer: No: hot weather affects both

ChallengeCan r be 1.5?

Answer: No