If θ be the acute angle between two regression line in the case of two variables x and y Show that tan θ=((1−r)/r).((σ_x σ_y )/(σ_x ^2 +σ_y ^2 )) where r,σ_x ,σ_y have their usual meanings. Explain the significance where r=0 and r=±r 1/2/2024


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

$I f θ b e t h e a c u t e a n g l e b e t w e e n t w o r e g r e s s i o n$ $l i n e i n t h e c a s e o f t w o v a r i a b l e s x a n d y$ $S h o w t h a t$ $\tan θ = \frac{1 - r}{r} . \frac{σ_{x} σ_{y}}{σ_{x}^{2} + σ_{y}^{2}}$ $w h e r e r, σ_{x}, σ_{y} h a v e t h e i r u s u a l m e a n i n g s .$ $E x p l a i n t h e s i g n i f i c a n c e w h e r e r = 0 a n d r = \pm r$ $1 / 2 / 2024$
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