If r is negative both the variables are decreasing.

Answer

To determine the truth of the statement "If r is negative, both the variables are decreasing," we can analyze the concept of correlation and its implications.

### Step-by-Step Solution:

1. **Understanding Correlation**:
- Correlation measures the relationship between two variables. It is represented by the correlation coefficient \( r \), which can range from -1 to 1.
- A positive correlation ( \( r > 0 \) ) indicates that as one variable increases, the other variable also increases. Conversely, if one decreases, the other also decreases.
- A negative correlation ( \( r < 0 \) ) indicates that as one variable increases, the other variable decreases. Conversely, if one decreases, the other increases.

2. **Analyzing the Statement**:
- The statement claims that if \( r \) is negative, then both variables are decreasing.
- However, from the definition of negative correlation, we know that if one variable decreases, the other must increase.

3. **Conclusion**:
- Therefore, the statement "If r is negative, both the variables are decreasing" is false. In a negative correlation, one variable's decrease corresponds to the other variable's increase.

### Final Answer:
The statement is **false**.

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