Mean of x= 53
Mean of y = 28
Regression coefficient of y on x = - 1.2
Regression coefficient of x on y= - 0.3
`r = square`

Answer

To find the value of \( r \) given the means and regression coefficients, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mean of \( x \) (\( \bar{x} \)) = 53
- Mean of \( y \) (\( \bar{y} \)) = 28
- Regression coefficient of \( y \) on \( x \) (\( b_{yx} \)) = -1.2
- Regression coefficient of \( x \) on \( y \) (\( b_{xy} \)) = -0.3

2. **Use the Relationship Between Regression Coefficients and Correlation Coefficient:**
The relationship between the regression coefficients and the correlation coefficient \( r \) is given by:
\[ r^2 = b_{xy} \times b_{yx} \]

3. **Substitute the Values:**
Substitute the values of \( b_{xy} \) and \( b_{yx} \):
\[ r^2 = (-0.3) \times (-1.2) \]

4. **Calculate \( r^2 \):**
Calculate the product:
\[ r^2 = 0.3 \times 1.2 = 0.36 \]

5. **Find \( r \):**
To find \( r \), take the square root of \( r^2 \):
\[ r = \sqrt{0.36} = 0.6 \]

6. **Determine the Sign of \( r \):**
Since both regression coefficients \( b_{xy} \) and \( b_{yx} \) are negative, \( r \) will also be negative:
\[ r = -0.6 \]

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