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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
144000
160000
F
320
290
92800
102400
84100
G
280
250
70000
78400
62500
H
410
155800
168100
J
240
91200
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:
Workings:
x¯ = 4020/10 = 402
y¯ = 3550/10 = 355
= 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.
L.H.S. =cos 12+cos 60+cos 84 =cos 12+(cos 84+cos 60) =cos 12+2.cos 72 . cos 12 =(1+2sin 18)cos 12 =(1+2.(√5 -1)/4)cos 12 =(1+.(√5 -1)/2)cos 12 =(√5 +1)/2.cos 12 R.H.S =c
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