If the angle between two lines regression is `90^(@)`, then it represents

Options

A. a perfect positive correlation
B. perfect negative correlation
C. no linear correlation i.e, r=0
D. None of these

Answer

To solve the question, we need to understand the relationship between the angle between two lines of regression and the correlation coefficient \( r \).

### Step-by-Step Solution:

1. **Understanding the Angle Between Regression Lines**:
The angle \( \theta \) between the two lines of regression can be calculated using the formula:
\[ \tan(\theta) = \frac{1 - r^2}{r} \]
where \( r \) is the correlation coefficient.

2. **Setting the Angle to 90 Degrees**:
If the angle \( \theta \) is \( 90^\circ \), then:
\[ \tan(90^\circ) \text{ is undefined.} \]
However, in the context of regression, we can also consider that \( \tan(90^\circ) \) approaches infinity, which implies that the denominator in the formula must equal zero.

3. **Finding the Condition for \( r \)**:
For \( \tan(\theta) \) to be undefined, the denominator \( r \) must be zero:
\[ r = 0 \]

4. **Interpreting the Correlation Coefficient**:
A correlation coefficient \( r = 0 \) indicates that there is no linear correlation between the two variables. This means that the two variables do not have a linear relationship.

5. **Conclusion**:
Therefore, when the angle between the two lines of regression is \( 90^\circ \), it represents **no linear correlation**.

### Final Answer:
The correct option is: **no linear correlation** (Option C).