Question

if the tangent of the angle between the lines of regression of Y on 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

The question that is being asked by you, If the tangent of the angle between the lines of regression of Y on 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.

This question requires some serious sort of stuff and this calculation cannot be done here without the help of proper mathematical annotations.

Answer 2

Answer:0.3

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