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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.
Determine y′ for xy = 1 . Solution : There are in fact two solution methods for this problem. Solution 1: It is the simple way of doing the problem. Just solve for y to
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