The coefficient of correlation when coefficients of regression are 0.2 and 1.8 is

Options

A. `0.36`
B. `0.2`
C. `0.6`
D. `0.9`

Explanation

To find the coefficient of correlation (r) when the coefficients of regression are given as 0.2 and 1.8, we can follow these steps:

### Step 1: Understand the relationship between regression coefficients and correlation coefficient
The coefficient of correlation (r) can be calculated using the formula:
\[ r = \sqrt{b_{xy} \cdot b_{yx}} \]
where \( b_{xy} \) is the regression coefficient of Y on X and \( b_{yx} \) is the regression coefficient of X on Y.

### Step 2: Identify the given regression coefficients
From the question, we have:
- \( b_{xy} = 0.2 \)
- \( b_{yx} = 1.8 \)

### Step 3: Substitute the values into the formula
Now we substitute the values into the correlation formula:
\[ r = \sqrt{0.2 \cdot 1.8} \]

### Step 4: Calculate the product
First, we calculate the product:
\[ 0.2 \cdot 1.8 = 0.36 \]

### Step 5: Take the square root
Now, we take the square root of the product:
\[ r = \sqrt{0.36} = 0.6 \]

### Step 6: Determine the sign of the correlation coefficient
Since both regression coefficients (0.2 and 1.8) are positive, the correlation coefficient will also be positive. Thus, we conclude:
\[ r = 0.6 \]

### Final Answer
The coefficient of correlation is \( r = 0.6 \).

---