Calculate the rank correlation co-efficient between - X - and - Y - variables-X - 10 - 20 - 35 - 14 - 18 - 21 - 16 illhlineY - 15 - 25 - 18 - 19 - 20 - 26 - 2711 hlinelend array

[ X amp;R_1 amp;Y amp;R_2 amp;D=R_1 R_2 amp;D^2; 10 amp;7 amp;15 amp;7 ...

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Standard XI

Statistics

Calculation of Correlation Coefficient

Calculate the...

Question

Calculate the rank correlation co-efficient between 'X' and 'Y' variables.

$\begin{matrix} X & 10 & 20 & 35 & 14 & 18 & 21 & 16 Y & 15 & 25 & 18 & 19 & 20 & 26 & 27 \end{matrix}$

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Solution

$\begin{matrix} X & R_{1} & Y & R_{2} & D = R_{1} - R_{2} & D^{2} 10 & 7 & 15 & 7 & 0 & 0 20 & 3 & 25 & 3 & 0 & 0 35 & 1 & 18 & 6 & - 5 & 25 14 & 6 & 19 & 5 & + 1 & 1 18 & 4 & 20 & 4 & 0 & 0 21 & 2 & 26 & 2 & 0 & 0 16 & 5 & 27 & 1 & + 4 & 16 \sum D = 0 & \sum D^{2} = 42 \end{matrix}$

$R = 1 - \frac{6 \sum D^{2}}{N (N^{2} - 1)} = 1 - \frac{6 \times 42}{7 (7^{2} - 1)} = 1 - \frac{252}{336} = 1 - 0.75 = 0.25$

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254

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Calculate the rank correlation co-efficient between 'X' and 'Y' variables. X10203514182116Y15251819202627

XR1YR2D=R1−R2D21071570020325300351186−525146195+111842040021226200165271+416∑D=0∑D2=42 R=1−6∑D2N(N2−1)=1−6×427(72−1)=1−252336=1−0.75=0.25

Calculate the rank correlation co-efficient between 'X' and 'Y' variables.

$\begin{matrix} X & 10 & 20 & 35 & 14 & 18 & 21 & 16 Y & 15 & 25 & 18 & 19 & 20 & 26 & 27 \end{matrix}$