Calculate Karl Pearsons Coefficient Of Correlation
Sample question: compute the value of the correlation coefficient from the following table:
Height 
139 
165 
162 
190 
182 
175 
125 
198 
136 
178 
Weight 
47 
53 
58 
86 
62 
68 
60 
91 
51 
84 
Solution:
Pearson’s Coefficient computational formula
Height (X) 
Weight (Y) 
dx=(XMean) 
dy=(Ymean) 
dx^2 
dy^2 
dx*dy 
139 
47 
26 
19 
676 
361 
494 
165 
53 
0 
13 
0 
169 
0 
162 
58 
3 
8 
9 
64 
24 
190 
86 
25 
20 
625 
400 
500 
182 
62 
17 
4 
289 
16 
68 
175 
68 
10 
2 
100 
4 
20 
125 
60 
40 
6 
1600 
36 
240 
198 
91 
33 
25 
1089 
625 
825 
136 
51 
29 
15 
841 
225 
435 
178 
84 
13 
18 
169 
324 
234 
∑X =1650 
∑ Y =660 


∑ x^{2} =5398 
∑ y^{2} =2224 
∑xy =2704 
n=10 
n=10 





mean=165 
mean=66 





r = (∑xy)/(√(n&(∑x2)/n)× √((∑y2)/n)) = (+ 2704)/(√(10&5398/10)× √(2224/10))
= (+ 2704)/(10×23.233×14.913)= (+ 2704)/3464.737 = 0.7804
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