Question
Download Solution PDFदिया गया x = 2y + 4 और y = kx + 6 क्रमशः y पर x और x पर y की समाश्रयण रेखाएं हैं।
यदि r का मान 0.5 है, तो k का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
सहसंबंध गुणांक समाश्रयण गुणांकों के बीच ज्यामितीय माध्य है अर्थात्
\({\rm{r}} = \pm \sqrt {{{\rm{b}}_{{\rm{yx}}}}{{\rm{b}}_{{\rm{xy}}}}} \)
गणना:
दिया गया समीकरण x = 2y + 4 और y = kx + 6 हैं।
\({{\rm{b}}_{{\rm{yx}}}} = k\) और \({{\rm{b}}_{{\rm{xy}}}} = 2\)
\({\rm{r}} = \pm \sqrt {{{\rm{b}}_{{\rm{yx}}}}{{\rm{b}}_{{\rm{xy}}}}} \)
\(\frac{1}{2} = \pm \sqrt {{{\rm{b}}_{{\rm{yx}}}} \times 2} \) ( दोनों पक्षों का वर्ग करने पर)
\(2{{\rm{b}}_{{\rm{yx}}}} = \frac{1}{4}\) ⇒ \({{\rm{b}}_{{\rm{yx}}}} = \frac{1}{8}\)
∴ \({{\rm{b}}_{{\rm{yx}}}} = k = \frac{1}{8}\)
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