Question

Find regression coefficient of y on x (byx) if correlation coefficient between x and y values is 0.75 and standard deviation of x and y are 5 and 6.4 respectively. 
1. 0.96
2. 0.59
3. 1.04
4. 1.7

Answer 1

Correct Answer - Option 1 : 0.96

Given 

Correlation coefficient between x on y = 0.75

Standard deviation of x and y = 5 and 6.4

Formula

Correlation coefficient ‘r’ = Cov(x,y)/S_xS_y

Cov(x,y) = Coveriance of x and y

S_x = Standard deviation of x

S_y = Standard deviation of y

Correlation coefficient of y on x = b_yx = Cov(x,y)/S_x²

Calculation

0.75 = Cov(x,y)/5 × 6.4

⇒ Cov(x,y) = 0.75 × 5 × 6.4

⇒ Cov(x,y) = 24

⇒ b_yx = 24/5²

∴ b_yx = 24/25

∴ correlation coefficient of y on x is 0.96