Answer: The Pearson correlation is appropriate for linear dependence, while Spearman rank correlation and Kendall's τ can deal with monotonic relationship.

## Explanation Let's analyze each option: **Option A: Incorrect** A zero Pearson correlation only indicates no **linear** relationship. There could still be non-linear relationships present. **Option B: Incorrect** Spearman rank correlation and Kendall's τ measure **monotonic** relationships, not all types of non-linear relationships. They cannot detect non-monotonic non-linear relationships. **Option C: Correct** - **Pearson correlation**: Measures linear dependence between variables - **Spearman rank correlation**: Measures monotonic relationships (whether linear or non-linear, as long as the relationship is consistently increasing or decreasing) - **Kendall's τ**: Also measures monotonic relationships, similar to Spearman but using a different calculation method **Option D: Incorrect** Significant differences between Pearson and rank correlations actually suggest the **presence** of non-linear relationships, not their absence. Therefore, option C is the correct statement.

Author: LeetQuiz Editorial Team