Question
Download Solution PDFमान लीजिये कि rxy दो चर राशियों X और Y के बीच सहसंबंध गुणांक है
जहाँ s.d.(X) = s.d.(Y)। यदि θ X पर Y और Y पर X समाश्रयण रेखाओं के बीच कोण है:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसूत्र
यदि θ समाश्रयण रेखाओं के बीच कोण है, तब
Tan θ = [(1 - r2)/r] × (σx × σy)/(σx2 + σy2)
व्याख्या
प्रश्न एक अनुसार
⇒ 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]
∴ \(sin \theta=\sqrt{\dfrac{1-r^2_{xy}}{1+r^2_{xy}}}\)
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