Answer: They do not have any linear relationship between them

## Explanation Correlation measures the **linear relationship** between two variables. A zero correlation indicates that there is **no linear relationship** between the variables. ### Key Points: 1. **Correlation (ρ) = 0** means the variables have **zero linear dependence**. 2. However, this **does not necessarily mean independence** - the variables could still have a **non-linear relationship** (e.g., quadratic, parabolic, or other functional forms). 3. Examples given in the text: - A symmetric parabola: Corr(X, Y) = 0 - A symmetric V-shape graph: Corr(X, Y) = 0 Both show non-linear relationships despite zero correlation. ### Why Other Options Are Incorrect: - **A**: Incorrect - Zero correlation does not guarantee independence; variables can be dependent in non-linear ways. - **C**: Incorrect - Zero correlation indicates the absence of linear dependence, not linear dependence. - **D**: Incorrect - A negative linear relationship would have correlation < 0, not = 0. ### Statistical Insight: Correlation coefficient (ρ) ranges from -1 to +1: - ρ = 0: No linear relationship - ρ > 0: Positive linear relationship - ρ < 0: Negative linear relationship Zero correlation only eliminates linear patterns, leaving the possibility of other functional relationships intact.

Author: Nikitesh Somanthe