If the line of regression of x on y is `3x + 2y - 5 = 0`, then the value of `b_(xy)` is

Options

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

Answer

To find the value of \( b_{xy} \) (the linear regression coefficient of \( x \) on \( y \)), we start with the given line of regression equation:

\[ 3x + 2y - 5 = 0 \]

### Step 1: Rearranging the equation
First, we will rearrange the equation to express \( x \) in terms of \( y \).

\[ 3x + 2y = 5 \]

### Step 2: Isolating \( x \)
Next, we isolate \( x \) by moving \( 2y \) to the other side:

\[ 3x = 5 - 2y \]

Now, divide each term by 3:

\[ x = \frac{5}{3} - \frac{2}{3}y \]

### Step 3: Identifying the slope
In the equation \( x = \frac{5}{3} - \frac{2}{3}y \), the coefficient of \( y \) (which is \(-\frac{2}{3}\)) represents the slope of the regression line of \( x \) on \( y \).

### Step 4: Finding \( b_{xy} \)
The linear regression coefficient \( b_{xy} \) is equal to the negative of the coefficient of \( y \) in the regression equation:

\[ b_{xy} = -\left(-\frac{2}{3}\right) = \frac{2}{3} \]

### Final Answer
Thus, the value of \( b_{xy} \) is:

\[ \boxed{\frac{2}{3}} \]

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