If `y = 5 - 2.8x` and `x = 3 – 0.5y` be the regression lines ,then the value of `b_(yx)` is

Options

A. `-0.5`
B. `-2.8`
C. `-0.5`
D. `-2`

Answer

To find the value of \( b_{yx} \) given the regression lines \( y = 5 - 2.8x \) and \( x = 3 - 0.5y \), we can follow these steps:

### Step 1: Identify the regression lines
We have two regression lines:
1. \( y = 5 - 2.8x \) (let's assume this is the regression line of \( y \) on \( x \))
2. \( x = 3 - 0.5y \) (let's assume this is the regression line of \( x \) on \( y \))

### Step 2: Determine the coefficients
From the first regression line \( y = 5 - 2.8x \), we can identify the slope \( b_{yx} \):
\[ b_{yx} = -2.8 \]

From the second regression line \( x = 3 - 0.5y \), we can identify the slope \( b_{xy} \):
\[ b_{xy} = -0.5 \]

### Step 3: Use the relationship between the regression coefficients
The relationship between the regression coefficients is given by:
\[ r^2 = b_{xy} \cdot b_{yx} \]
where \( r \) is the correlation coefficient.

### Step 4: Calculate \( b_{yx} \)
Since we have identified \( b_{yx} \) from the regression line of \( y \) on \( x \):
\[ b_{yx} = -2.8 \]

### Step 5: Final answer
Thus, the value of \( b_{yx} \) is:
\[ \boxed{-2.8} \]