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=(X-Mean) |
dy=(Y-mean) |
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 |
|
|
∑ x2 =5398 |
∑ y2 =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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