If for a bivariate data, `b_(yx)= -1.2` and `b_(xy)=-0.3` then `r` =

Options

A. `-0.06`
B. `0.06`
C. `0.6`
D. `-0.6`

Answer

To find the correlation coefficient \( r \) given the regression coefficients \( b_{yx} \) and \( b_{xy} \), we can follow these steps:

### Step 1: Identify the given values
We are given:
- \( b_{yx} = -1.2 \) (regression coefficient of \( y \) on \( x \))
- \( b_{xy} = -0.3 \) (regression coefficient of \( x \) on \( y \))

### Step 2: Use the relationship between regression coefficients and correlation coefficient
The relationship between the regression coefficients and the correlation coefficient is given by the formula:
\[ r^2 = b_{xy} \cdot b_{yx} \]

### Step 3: Substitute the values into the formula
Substituting the given values into the formula:
\[ r^2 = (-0.3) \cdot (-1.2) \]

### Step 4: Calculate \( r^2 \)
Calculating the product:
\[ r^2 = 0.3 \cdot 1.2 = 0.36 \]

### Step 5: Take the square root to find \( r \)
To find \( r \), we take the square root of \( r^2 \):
\[ r = \sqrt{0.36} \]
This gives us:
\[ r = 0.6 \quad \text{or} \quad r = -0.6 \]

### Step 6: Determine the sign of \( r \)
Since both regression coefficients \( b_{yx} \) and \( b_{xy} \) are negative, the correlation coefficient \( r \) will also be negative:
\[ r = -0.6 \]

### Final Answer
Thus, the correlation coefficient \( r \) is:
\[ \boxed{-0.6} \]