Given `b_(yx) = 1.9, b_(xy) = 0.47`, then coefficient of correlation =

Options

A. `(19)/(10)`
B. `-(19)/(10)`
C. `-(10)/(19)`
D. `(19)/(20)`

Answer

To find the coefficient of correlation given \( b_{yx} = 1.9 \) and \( b_{xy} = 0.47 \), we can use the formula for the coefficient of correlation \( r \):

\[ r = \sqrt{b_{xy} \cdot b_{yx}} \]

### Step 1: Substitute the values into the formula
We have:
- \( b_{xy} = 0.47 \)
- \( b_{yx} = 1.9 \)

Substituting these values into the formula gives us:

\[ r = \sqrt{0.47 \cdot 1.9} \]

### Step 2: Calculate the product
Now, we need to calculate the product \( 0.47 \cdot 1.9 \):

\[ 0.47 \cdot 1.9 = 0.893 \]

### Step 3: Take the square root
Next, we take the square root of \( 0.893 \):

\[ r = \sqrt{0.893} \approx 0.945 \]

### Step 4: Convert to fraction form
To express \( r \) in fraction form, we can approximate \( 0.945 \) as \( \frac{19}{20} \).

### Final Answer
Thus, the coefficient of correlation is:

\[ r = \frac{19}{20} \]