If the regression coefficients `b_(xy)=1.6` and `b_(yx)=0.4`, and `theta` is the angle between the two lines of regression, then the value of `tantheta` is

Options

A. A) -0.36
B. B) 0.72
C. C) -0.18
D. D) 0.64

Answer

To find the value of \( \tan \theta \) given the regression coefficients \( b_{xy} = 1.6 \) and \( b_{yx} = 0.4 \), we will use the formula:

\[ \tan \theta = \frac{b_{xy} \cdot b_{yx} - 1}{b_{xy} + b_{yx}} \]

### Step-by-Step Solution:

1. **Identify the given values**:
- \( b_{xy} = 1.6 \)
- \( b_{yx} = 0.4 \)

2. **Substitute the values into the formula**:
\[ \tan \theta = \frac{(1.6)(0.4) - 1}{1.6 + 0.4} \]

3. **Calculate the numerator**:
- First, calculate \( (1.6)(0.4) \):
\[ 1.6 \times 0.4 = 0.64 \]
- Now, substitute this value into the numerator:
\[ 0.64 - 1 = -0.36 \]

4. **Calculate the denominator**:
- Now, calculate \( 1.6 + 0.4 \):
\[ 1.6 + 0.4 = 2.0 \]

5. **Combine the results**:
\[ \tan \theta = \frac{-0.36}{2.0} \]

6. **Final calculation**:
- Now, divide:
\[ \tan \theta = -0.18 \]

### Conclusion:
The value of \( \tan \theta \) is \( -0.18 \).