If-be-the-acute-angle-between-two-regression-line-in-the-case-of-two-variables-x-and-y-Show-that-tan-1-r-r-x-y-x-2-y-2-where-r-x-y-have-their-usual-meanings-Ex

Question Number 192255 by Spillover last updated on 01/Feb/24

I f θ b e t h e a c u t e a n g l e b e t w e e n t w o r e g r e s s i o n

l i n e i n t h e c a s e o f t w o v a r i a b l e s x a n d y

S h o w t h a t

\tan θ = \frac{1 - r}{r} . \frac{σ_{x} σ_{y}}{σ_{x}^{2} + σ_{y}^{2}}

w h e r e r, σ_{x}, σ_{y} h a v e t h e i r u s u a l m e a n i n g s .

E x p l a i n t h e s i g n i f i c a n c e w h e r e r = 0 a n d r = \pm r

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