If r12 = 0.8, r13 = 0.77 and r23 = 0.69 then find R2.13 and r23.1

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Solution:

r12 = 0.8

r13 = 0.77

r23 = 0.69

R2.13 = ?

r23.1 = ?

We know that,

\(R_{2.13} = \sqrt{\frac{r_{12}^2 + r_{13}^2 + 2.r_{12}.r_{13}.r_{23} }{1 – r_{13}^2}}\)

\(= \sqrt{\frac{0.8^2 + 0.77^2 + 2 \times 0.8 \times 0.69 \times 0.77}{1 – 0.77^2}}\)

\(= \sqrt{\frac{2.08298}{0.4071}}\)

= 2.26

And,

\(r_{23.1} = \frac{ r_{23} – r_{12}.r_{13} }{\sqrt{(1-r_{12}^2) (1-r_{13}^2) }}\)

\(= \frac{ 0.69 – 0.8 \times 0.77 }{\sqrt{(1-0.8^2) (1-0.77^2) }}\)

\(= \frac{0.074}{0.383}\)

= 0.193

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