Regression equation of Y on X 2x+3y-12=0. The value of byx is

Options

A. `-2//3`
B. `-3//2`
C. `2//3`
D. `3//2`

Answer

To find the value of the regression coefficient \( b_{yx} \) from the regression equation of \( Y \) on \( X \), given by the equation \( 2x + 3y - 12 = 0 \), we can follow these steps:

### Step 1: Rearranging the Equation
We start with the regression equation:
\[ 2x + 3y - 12 = 0 \]

We can rearrange this equation to express \( y \) in terms of \( x \):
\[ 3y = 12 - 2x \]

### Step 2: Solve for \( y \)
Now, we divide the entire equation by 3 to isolate \( y \):
\[ y = \frac{12}{3} - \frac{2}{3}x \]
\[ y = 4 - \frac{2}{3}x \]

### Step 3: Identify the Coefficient of \( x \)
In the equation \( y = 4 - \frac{2}{3}x \), we can identify the coefficient of \( x \). The coefficient of \( x \) is:
\[ -\frac{2}{3} \]

### Step 4: Determine \( b_{yx} \)
The coefficient of \( x \) in the regression equation of \( Y \) on \( X \) is equal to \( b_{yx} \):
\[ b_{yx} = -\frac{2}{3} \]

### Final Answer
Thus, the value of \( b_{yx} \) is:
\[ \boxed{-\frac{2}{3}} \]

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