If `b_(xy)=-(3)/(2),b_(yx)=-(1)/(6)`, then value of r is ……………..

Answer

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

### Step 1: Write down the given values
We have:
- \( b_{xy} = -\frac{3}{2} \)
- \( b_{yx} = -\frac{1}{6} \)

### Step 2: Use the formula for the correlation coefficient
The correlation coefficient \( r \) is related to the regression coefficients by the formula:
\[ r = \sqrt{b_{xy} \cdot b_{yx}} \]

### Step 3: Substitute the values into the formula
Substituting the given values into the formula:
\[ r = \sqrt{\left(-\frac{3}{2}\right) \cdot \left(-\frac{1}{6}\right)} \]

### Step 4: Simplify the expression inside the square root
Calculating the product:
\[ -\frac{3}{2} \cdot -\frac{1}{6} = \frac{3}{12} = \frac{1}{4} \]

### Step 5: Take the square root
Now, we take the square root:
\[ r = \sqrt{\frac{1}{4}} = \frac{1}{2} \]

### Step 6: Determine the sign of \( r \)
Since both regression coefficients \( b_{xy} \) and \( b_{yx} \) are negative, the correlation coefficient \( r \) will also be negative:
\[ r = -\frac{1}{2} \]

### Final Answer
Thus, the value of \( r \) is:
\[ \boxed{-\frac{1}{2}} \]

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