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Calculate the Spearman’S Rank Correlation Coefficient for the Following Data and Interpret the Result: - Mathematics

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Sum

Calculate the Spearman’s rank correlation coefficient for the following data and interpret the result: 

X 35 54 80 95 73 73 35 91 83 81
Y 40 60 75 90 70 75 38 95 75 70
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Solution

To determine Spearman’s Rank Correlation:

X Y R1 R2 d = R1 - R2 d2
35 40 9.5 9 0.5 0.25
54 60 8 8 0 0
80 75 5 4 1 1
95 90 1 2 -1 1
73 70 6.5 6.5 0 0
73 75 6.5 4 2.5 6.25
35 38 9.5 10 -0.5 0.25
91 95 2 1 1 1
83 75 3 4 -1 1
81 70 4 6.5 -2.5 6.25
Total         ∑d2 = 17

r = 1 - `(6[sum"d"^2 + sum (("t"^3 - "t")/12)])/("N"("N"^2 - 1))`

where t is the number of individual involved in a tie.

Here, ∑d2 = 17, N = 10 , t = 3,2,2,2

`sum("t"^3-"t")/12 = ((3)^2 - 3)/12 + 3 xx ((2)^3 - 2)/12`


`= (27-3)/12 + 3 xx (8 - 2)/12`

 

`= 24/12 + 18/12 = 42/12 =7/2 = 3.5` 


r = `1 - (6[17 + 3.5])/(10(100 - 1))`


`=1 - 123/990`


`= (990-123)/990`


`= 867/990 = 0.876` 

Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
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