Answer: They do not have any linear relationship between them

## Explanation **Correct Answer: B** A zero correlation (ρ = 0) between two variables specifically indicates that there is **no linear relationship** between them. However, this does not necessarily mean the variables are independent. ### Key Points: - **Correlation measures linear relationships only** - It quantifies how well two variables can be described by a straight line - **Independence vs. Zero Correlation**: - If two variables are independent, they must have zero correlation - However, zero correlation does NOT guarantee independence - Variables can have zero correlation but still be related through nonlinear relationships ### Example: Consider the relationship between X and Y = X². If X is symmetric around zero (e.g., normally distributed), the correlation between X and X² will be zero, but they are clearly not independent - Y is completely determined by X. Therefore, option B is correct because zero correlation specifically means no linear relationship exists, while option A is incorrect because zero correlation doesn't guarantee independence.

Author: Tanishq Prabhu