Empirical Covariance

• sxy
  1/n * (sum((x - mean(x)) * (y - mean(y))))
• sxx
  1/n * (sum((x - mean(x)) * (x - mean(y))))

• Interpretation

• With a positive linear relationship between 𝑋 and 𝑌, we obtain sxy > 0 (positive covariance)
• With a negative linear relationship between 𝑋 and 𝑌, we obtain sxy < 0 (negative covariance)
• If there is no linear relationship between 𝑋 and 𝑌, then sxy ≈ 0

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