While calculating the coefficient of correlation between two variables x and y, the
following results were obtained: n=25, Σx=125, Σy=100, ΣΧ2 =650.Σy2 =460, Σ
xy=508. It was however later discovered at the time of checking that two pairs of
observations (x,y) were copied (6,14) and (8,6) while the correct were (8,12) and
(6,8) respectively. Determine the correct value of correlation.
Answers
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9
Answer:
Corrected ∑x=125−6−8+8+6=125
Corrected ∑y=100−14−6+12+8=100
Corrected ∑x
2
=650−(6)
2
−(8)
2
+(6)
2
+(8)
2
=650
Corrected ∑y
2
=460−(14)
2
−(6)
2
+(12)
2
+(8)
2
=436
Corrected ∑xy=508−6×18−8×6+8×12+6×8=520
The formula for Pearson product moment correlation is
r=
[n∑x
2
−(∑x)
2
][n∑y
2
−(∑y)
2
]
n∑xy−(∑x)(∑y)
=
[25×650−(125)
2
][25×436−(100)
2
]
25×520−125×100
=
[16250−15625][10900−10000]
13000−12500
=
[625][900]
500
=
(25)(30)
500
=
3
2
=0.667
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