For the following data consists r12 = 0.8, r23 = 0.9 and r13 = 0.82 find the r23.1 and R1.23 interpreted the results.

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Solution:

r12 = 0.8

r23 = 0.9

r13 = 0.82

r23.1 = ?

R1.23 = ?

We know

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

\(= \frac{0.9 – 0.8 \times 0.82}{ \sqrt{ (1-0.8^2) (1-0.9^2) } }\)

= 0.933

\(R_{1.23} = \sqrt{\frac{ r_{12}^2 + r_{13}^2 – 2 \times r_{12} \times r_{23} \times r_{13} }{ 1 – r_{23}^2 }}\)

\( = \sqrt{\frac{ 0.8^2 + 0.82^2 – 2 \times 0.8 \times 0.9 \times 0.82 }{ 1 – 0.82^2 }}\)

= 0.634

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