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 y = 25
`x-square=square(25- square)`
`:. x = square`

Answer

To solve the problem step by step, we will use the given information about the means and regression coefficients.

### Step 1: Write down the given information
- Mean of \( x \) (\( \bar{x} \)) = 53
- Mean of \( y \) (\( \bar{y} \)) = 28
- Regression coefficient of \( y \) on \( x \) (\( b_{y|x} \)) = -1.2
- Regression coefficient of \( x \) on \( y \) (\( b_{x|y} \)) = -0.3
- Given \( y = 25 \)

### Step 2: Use the regression equation of \( x \) on \( y \)
The regression equation of \( x \) on \( y \) is given by:

\[ x - \bar{x} = b_{x|y} \cdot (y - \bar{y}) \]

Substituting the known values:

\[ x - 53 = -0.3 \cdot (y - 28) \]

### Step 3: Substitute \( y = 25 \)
Now, substitute \( y = 25 \) into the equation:

\[ x - 53 = -0.3 \cdot (25 - 28) \]

### Step 4: Simplify the right side
Calculate \( 25 - 28 \):

\[ 25 - 28 = -3 \]

Now substitute this back into the equation:

\[ x - 53 = -0.3 \cdot (-3) \]

### Step 5: Calculate the right side
Calculate \( -0.3 \cdot (-3) \):

\[ -0.3 \cdot (-3) = 0.9 \]

So, we have:

\[ x - 53 = 0.9 \]

### Step 6: Solve for \( x \)
Now, add 53 to both sides to find \( x \):

\[ x = 53 + 0.9 \]

\[ x = 53.9 \]

### Final Answer
Thus, the value of \( x \) when \( y = 25 \) is:

\[ \boxed{53.9} \]

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