Answer: a linear relationship between the variables only.

## Explanation A zero correlation (correlation coefficient = 0) specifically indicates the absence of a **linear** relationship between two variables. However, it does NOT necessarily imply the absence of a non-linear relationship. ### Key Points: 1. **Correlation measures linear association** - The correlation coefficient (Pearson's r) quantifies the strength and direction of a linear relationship between two variables. 2. **Zero correlation means no linear pattern** - When r = 0, there is no straight-line relationship between the variables. 3. **Non-linear relationships can exist** - Variables can have strong non-linear relationships (e.g., quadratic, exponential, sinusoidal) while still having zero linear correlation. ### Example: Consider the relationship y = x². If x ranges symmetrically around zero (e.g., -3, -2, -1, 0, 1, 2, 3), the correlation between x and y will be approximately zero, even though there is a perfect quadratic relationship. ### Why other options are incorrect: - **Option B**: Incorrect because zero correlation doesn't rule out non-linear relationships. - **Option C**: Incorrect because zero correlation only rules out linear relationships, not necessarily non-linear ones. Therefore, the correct answer is **A** - a zero correlation implies the absence of a linear relationship only.

Author: LeetQuiz .