जर x आणि y मधील सहसंबंध गुणांक 0.5 असेल आणि y चा x वरील प्रतिगमन गुणांक 0.5 असेल, तर x चा y वरील प्रतिगमन गुणांक किती असेल?

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SSC CGL Tier-II (JSO) 2022 Official Paper (Held On: 4 March 2023)
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  1. 0.05
  2. 0.5
  3. 1
  4. 0.25

Answer (Detailed Solution Below)

Option 2 : 0.5
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योग्य उत्तर 0.5 आहे.
 Key Points  दिलेले आहे,
x आणि y मधील सहसंबंध गुणांक (rxy) = 0.5
y चा x वरील प्रतिगमन गुणांक (byx) = 0.5
x चा y वरील प्रतिगमन गुणांक (bxy) = \({r^2 \over b_{yx}}\) = \({(0.5)^2 \over 0.5} = 0.5\)
 Important Points

x आणि y मधील सहसंबंध गुणांक (rxy) = \(\sqrt {{b_{xy}} × {b_{yx}}}\)
किंवा, rxy2 = bxy x byx
किंवा, bxy = \({r^2 \over b_{yx}}\)
म्हणून, x चा y वरील प्रतिगमन गुणांकाचा आवश्यक मूल्य 0.5 आहे

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