Example of product moment correlation, Mathematics

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.

Posted Date: 2/16/2013 7:11:02 AM | Location : United States







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