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Question

Calculate Karl Pearson's Coefficient of Correlation on the following data:
X : 15 18 21 24 27 30 36 39 42 48
Y : 25 25 27 27 31 33 35 41 41 45

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Solution

X Y X-X
(x)
x2 Y-Y
(y)
y2 xy
15 25 −15 225 −8 64 120
18 25 −12 144 −8 64 96
21 27 −9 81 −6 36 54
24 27 −6 36 −6 36 36
27 31 −3 9 −2 4 6
30 33 0 0 0 0 0
36 35 6 36 2 4 12
39 41 9 81 8 64 72
42 41 12 144 8 64 96
48 45 18 324 12 144 216
ƩX = 300 ƩY =330 Ʃx2 =1080 Ʃy2 =480 Ʃxy =708

N = 10

X=ΣXN=30010=30Y=ΣYN=33010=33r=ΣxyΣx2 ×Σy2 =7081080× 480=70832.86×21.91 =708720 =0.983
Thus, the value of correlation coefficient is 0.983.

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