Mean of x= 53
Mean of y = 28
Regression coefficient of y on x = - 1.2
Regression coefficient of x on y= - 0.3
When x = 50 ,
`y-square=square(50- square)`
`:. y = square`

Answer

To solve the problem step by step, we will use the information provided and the regression equations.

### Step 1: Write down the given information
- 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

### Step 2: Write the regression equation of y on x
The regression equation of y on x can be expressed as:
\[ y - \bar{y} = b_{yx} (x - \bar{x}) \]
Substituting the values we have:
\[ y - 28 = -1.2 (x - 53) \]

### Step 3: Substitute the value of x
We need to find the value of y when \( x = 50 \):
\[ y - 28 = -1.2 (50 - 53) \]

### Step 4: Simplify the equation
Calculating \( 50 - 53 \):
\[ 50 - 53 = -3 \]
Now substitute this back into the equation:
\[ y - 28 = -1.2 \times (-3) \]

### Step 5: Calculate the right-hand side
Calculating \( -1.2 \times -3 \):
\[ y - 28 = 3.6 \]

### Step 6: Solve for y
Now, add 28 to both sides to solve for y:
\[ y = 28 + 3.6 \]
\[ y = 31.6 \]

### Final Answer
Thus, when \( x = 50 \), the value of \( y \) is \( 31.6 \).

---