If the regression coefficients y on x and x on y respectively are 0.8 and 0.2, what would be the value of coefficient of correlation?

Options

A. `1.6`
B. `0.4`
C. `0.1`
D. None of these

Answer

To find the coefficient of correlation given the regression coefficients, we can use the following steps:

### Step 1: Understand the given regression coefficients
We have:
- Regression coefficient of y on x (denoted as \( b_{yx} \)) = 0.8
- Regression coefficient of x on y (denoted as \( b_{xy} \)) = 0.2

### Step 2: Use the formula for the coefficient of correlation
The coefficient of correlation (denoted as \( r \)) can be calculated using the formula:
\[ r = \sqrt{b_{xy} \cdot b_{yx}} \]

### Step 3: Substitute the values into the formula
Now, we substitute the given values into the formula:
\[ r = \sqrt{0.2 \cdot 0.8} \]

### Step 4: Calculate the product
Calculate the product inside the square root:
\[ 0.2 \cdot 0.8 = 0.16 \]

### Step 5: Take the square root
Now, take the square root of 0.16:
\[ r = \sqrt{0.16} = 0.4 \]

### Conclusion
Thus, the value of the coefficient of correlation \( r \) is 0.4.

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