Question

show that the coefficient of correlation is the geometric mean of the two regression coefficient.​

Answer 1

Answer:

We know that regression coeff. of x on y=b

xy

=ρ

σ

y

σ

x

and regression coeff. of y on x=b

yx

=ρ

σ

x

σ

y

∴b

xy

.b

yx

=ρ

σ

y

σ

x

.ρ

σ

x

σ

y

=ρ

2

∴ρ=

b

xy

.b

yx

(Here ρ is correlation coefficient).