Pearson paired values
- Input
- Pairs: (1,2), (2,4), (3,5), (4,8), (5,10).
- Method
- Center x and y values, compute covariance, and divide by the product of standard deviations.
- Formula
- r = cov(x,y) / (s_x s_y)
- Intermediate steps
- x increases with y
- The centered products are mostly positive
- Final result
- Pearson r is strongly positive for this example.
- Interpretation
- The p-value tests whether the correlation differs from zero under assumptions.
- Limitation
- Correlation does not prove causation or rule out confounding.