Question
Download Solution PDFSuppose rxy is the correlation coefficient between two variables X and Y
where s.d.(X) = s.d.(Y). If θ is the angle between the two regression lines of Y on X and X on Y then:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula
If θ be the angle between the regression lines then,
Tan θ = [(1 - r2)/r] × (σx × σy)/(σx2 + σy2)
Explanation
According to question
⇒ σx = σy
⇒ Tanθ = [(1 - r2/r] × (σx2/(2σx)
⇒ Tanθ = [(1 - r2/r] × 1/2
⇒ Tan θ = (1 - r2/2r
⇒ Tanθ = Sinθ/cosθ
⇒ Tanθ = Sinθ × cosθ
⇒ Sinθ = Tanθ /secθ
⇒ Sinθ = Tanθ/√(1 + tan2θ)
⇒ Sinθ = [(1 - r2/r]/√(1 + (1 - r2/2r)2)
⇒ Sinθ = (1 - r2)/√[(1 - r2)2 + 4r2]
∴
Last updated on Jun 10, 2025
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