Question

If the tangent of the angle between the lines of regression of Yon X and X on Y is 0.6, and the
S.D. of Y is twice that of X, find the correlation coefficient between X and Y.​

Answer 1

Answer:

The answer is 0.3

Step-by-step explanation:

Let the angle made by Lyz with X-axis be θ

Tangent of the angle made by Lyz with X- axis = tan θ = 0.6

But , slope of any line with X-axis = tan θ

However, slope of Lyx= byx

byx = tan θ = 0.6

But byx=r σyσx

0.6=r 2σxσx−−−−−−−−(given)

0.6=2r

r=0.3

The correlation coefficient between x and y(r) = 0.3