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

### Step 1: Rearrange the equation
We start with the equation:
\[ 2x + 3y - 12 = 0 \]
We can rearrange it to isolate \( y \):
\[ 3y = 12 - 2x \]

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

### Step 3: Identify the slope
In the equation \( y = mx + c \), the coefficient of \( x \) (which is \( -\frac{2}{3} \)) represents the slope of the regression line of \( Y \) on \( X \). Therefore:
\[ b_{yx} = -\frac{2}{3} \]

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

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