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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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