If `r=0.5,sigma_x=3 ,sigma_y^2 =16 ` then `b_(xy) = .....`

Options

A. 0.375
B. 0.667
C. 2.667
D. 0.093

Answer

To find \( b_{xy} \), which is the coefficient of regression of \( x \) on \( y \), we can use the formula:

\[ b_{xy} = r \cdot \frac{\sigma_x}{\sigma_y} \]

where:
- \( r \) is the correlation coefficient,
- \( \sigma_x \) is the standard deviation of \( x \),
- \( \sigma_y \) is the standard deviation of \( y \).

Given:
- \( r = 0.5 \)
- \( \sigma_x = 3 \)
- \( \sigma_y^2 = 16 \)

First, we need to find \( \sigma_y \) from \( \sigma_y^2 \):

\[ \sigma_y = \sqrt{16} = 4 \]

Now, we can substitute the values into the formula:

\[ b_{xy} = 0.5 \cdot \frac{3}{4} \]

Next, we simplify the fraction:

\[ b_{xy} = 0.5 \cdot 0.75 \]

Calculating this gives:

\[ b_{xy} = 0.375 \]

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

\[ \boxed{0.375} \]