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### Correlation Analysis (Numeric Data)

- Correlation coefficient (also called Pearson’s product moment coefficient)

\[ {r_{A,B}}=\frac{\sum_{i=1}^{n} (a_{i}-\bar{A}) (b_{i}-\bar{B})}{(n-1)\sigma_{A} \sigma_{B}}=\frac{\sum_{i=1}^{n} (a_{i}b_{i})-n \bar{A}\bar{B}}{(n-1)\sigma_{A} \sigma_{B}} \]

where n is the number of tuples, and are the respective means of A and B, σA and σB are the respective standard deviation of A and B, and Σ(aibi) is the sum of the AB cross-product. - If rA,B > 0, A and B are positively correlated (A’s values increase as B’s). The higher, the stronger correlation.
- rA,B = 0: independent; rAB < 0: negatively correlated

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