Example of product moment correlation, Mathematics

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Example of Product moment correlation

The given data was acquired during a social survey conducted in a described urban area regarding the yearly income of described families and the corresponding expenditures.

Family

(x)Annual income £ 000

(y)Annual expenditure £ 000

xy

x2

Y2

A

420

360

151200

176400

129600

B

380

390

148200

144400

152100

C

520

510

265200

270400

260100

D

610

500

305000

372100

250000

E

400

360

144000

160000

129600

F

320

290

92800

102400

84100

G

280

250

70000

78400

62500

H

410

380

155800

168100

144400

J

380

240

91200

144400

57600

K

300

270

81000

90000

72900

Total

4020

3550

1504400

1706600

1342900

Required

Compute the product moment correlation coefficient briefly comment on the value acquired

The produce moment correlation:

1701_Example of Product moment correlation 1.png

Workings:

x¯  = 4020/10 = 402                 

y¯ = 3550/10 = 355

1442_Example of Product moment correlation 2.png

= 0.89

Comment: The value acquired 0.89 suggests that the correlation between annual expenditure and annual income is high and positive. This shows that the more one earns the more one spends.


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