If the two regression coefficients are - 0.4 and -1.6, then the coefficient of correlations is

Options

A. 0
B. `-0.9`
C. 0.8
D. 1

Answer

To find the coefficient of correlation given the two regression coefficients, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Regression Coefficients**:
Let the two regression coefficients be:
- \( r_{xy} = -0.4 \)
- \( r_{yx} = -1.6 \)

2. **Use the Formula for Coefficient of Correlation**:
The coefficient of correlation \( r \) can be calculated using the formula:
\[ r = \sqrt{r_{xy} \cdot r_{yx}} \]

3. **Substitute the Values**:
Substitute the values of \( r_{xy} \) and \( r_{yx} \) into the formula:
\[ r = \sqrt{(-0.4) \cdot (-1.6)} \]

4. **Calculate the Product**:
Calculate the product of the two regression coefficients:
\[ (-0.4) \cdot (-1.6) = 0.64 \]

5. **Take the Square Root**:
Now, take the square root of the product:
\[ r = \sqrt{0.64} = 0.8 \]

6. **Conclusion**:
Therefore, the coefficient of correlation is:
\[ r = 0.8 \]

### Final Answer:
The coefficient of correlation is \( 0.8 \).

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