If r is the coefficient of correlation between two variable, then

Options

A. `rge1`
B. `rle1`
C. `|r|le1`
D. `|r|ge1`

Answer

To solve the question regarding the coefficient of correlation \( r \) between two variables, we need to understand the properties and range of the correlation coefficient.

### Step-by-Step Solution:

1. **Understanding the Coefficient of Correlation**:
The coefficient of correlation \( r \) measures the strength and direction of a linear relationship between two variables. Its value can range from -1 to 1.

2. **Identifying the Range of \( r \)**:
- The maximum value of \( r \) is 1, which indicates a perfect positive correlation.
- The minimum value of \( r \) is -1, which indicates a perfect negative correlation.
- Therefore, we can conclude that:
\[ -1 \leq r \leq 1 \]

3. **Considering the Absolute Value**:
The absolute value of the correlation coefficient, denoted as \( |r| \), will always be less than or equal to 1, since:
\[ |r| \leq 1 \quad \text{(because } r \text{ is between -1 and 1)} \]

4. **Evaluating the Options**:
Given the options:
- Option 1: \( r \geq 1 \) (Incorrect)
- Option 2: \( r \leq 1 \) (Partially correct but not comprehensive)
- Option 3: \( |r| \leq 1 \) (Correct)
- Option 4: \( |r| \geq 1 \) (Incorrect)

The only option that accurately reflects the properties of the correlation coefficient is:
\[ |r| \leq 1 \]

5. **Conclusion**:
Therefore, the correct answer is:
\[ \text{Option 3: } |r| \leq 1 \]