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

= 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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