Question

If standard deviations of X and Y are 4 and 3 respectively and coefficient of correlation between X and Y is 0.8, then the regression coefficient of Y on X i.e. $b_{yx}$ is:

• A. 0.6
• B. 1.07
• C. 0.45
• D. 1.42

Hint:

Logic Tip: Regression coefficient depends on both correlation and ratio of standard deviations.

Answer 1

The Correct Option is A

Step 1:
Regression coefficient of $Y$ on $X$ is: \[ b_{yx}=r\left(\frac{\sigma_y}{\sigma_x}\right) \] where:
• $r =$ coefficient of correlation
• $\sigma_y =$ standard deviation of $Y$
• $\sigma_x =$ standard deviation of $X$

Step 2:
Given: \[ r=0.8 \] \[ \sigma_x=4 \] \[ \sigma_y=3 \] Substituting: \[ b_{yx}=0.8\left(\frac{3}{4}\right) \]

Step 3:
\[ b_{yx}=0.8 \times 0.75 \] \[ =0.6 \]

Step 4:
Therefore, the regression coefficient of $Y$ on $X$ is: \[ \boxed{0.6} \] Hence, the correct answer is: \[ \boxed{\text{(1) 0.6}} \]