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 strong non-linear relationships present - Example: Perfect quadratic relationship (parabola) can have zero Pearson correlation **Option B: Incorrect** - Spearman rank correlation and Kendall's τ measure *monotonic* relationships - They cannot capture all types of non-linear relationships - Non-monotonic relationships (like U-shaped curves) may not be detected **Option C: Correct** - Pearson correlation measures linear dependence between variables - Spearman rank correlation and Kendall's τ measure monotonic relationships (whether linear or non-linear, as long as they are monotonic) - This is the fundamental distinction between these correlation measures **Option D: Incorrect** - Significant differences between Pearson and rank correlations actually suggest the *presence* of non-linear relationships - If the relationship is purely linear, Pearson and rank correlations should be similar - Differences indicate the relationship may be monotonic but non-linear **Key Points:** - **Pearson**: Linear relationships only - **Spearman & Kendall**: Monotonic relationships (linear or non-linear) - Zero Pearson correlation ≠ No relationship - Differences between correlation measures suggest non-linearity

Author: LeetQuiz .