If the line of regression are parallel to the coordinate axis, then the coefficient of correlation is

Options

A. 1
B. 0
C. -1
D. `1/(2)`

Answer

To solve the question, we need to understand the relationship between the lines of regression and the coefficient of correlation.

### Step-by-Step Solution:

1. **Understanding the Lines of Regression**:
- In statistics, the line of regression represents the relationship between two variables. If the lines of regression are parallel to the coordinate axes, it indicates that one variable does not change with respect to the other.

2. **Identifying Parallel Lines**:
- If the lines of regression are parallel to the coordinate axes, it means that the slope of one line is zero. This indicates that the dependent variable does not vary with the independent variable.

3. **Coefficient of Correlation (r)**:
- The coefficient of correlation (r) quantifies the degree to which two variables are related. The value of r can range from -1 to +1.
- If r = 1, it indicates a perfect positive correlation, meaning that as one variable increases, the other variable also increases perfectly.
- If r = -1, it indicates a perfect negative correlation, meaning that as one variable increases, the other variable decreases perfectly.
- If r = 0, it indicates no correlation between the variables.

4. **Conclusion**:
- Since the lines of regression are parallel to the coordinate axes, it implies that there is a perfect correlation between the two variables. Therefore, the coefficient of correlation (r) must be equal to 1.

### Final Answer:
The coefficient of correlation is \( r = 1 \).

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