If the regression equation `x` on `y` is `3x+2y=26` then `b_(xy)` equals to

Options

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

Answer

To find the regression coefficient \( b_{xy} \) from the regression equation \( 3x + 2y = 26 \), we can follow these steps:

### Step 1: Rearrange the regression equation
Start with the given regression equation:
\[ 3x + 2y = 26 \]
We want to express \( x \) in terms of \( y \). To do this, isolate \( x \):
\[ 3x = 26 - 2y \]
Now, divide both sides by 3:
\[ x = \frac{26 - 2y}{3} \]

### Step 2: Simplify the equation
Rewrite the equation:
\[ x = -\frac{2}{3}y + \frac{26}{3} \]
This is now in the form \( x = b_{xy}y + a \), where \( b_{xy} \) is the slope of the line.

### Step 3: Identify the regression coefficient
From the equation \( x = -\frac{2}{3}y + \frac{26}{3} \), we can see that:
\[ b_{xy} = -\frac{2}{3} \]

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