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Correlation question

priya (Student) (64 Points)

25 May 2012

Please help me with this question..Thanks in advance.

Given that for 20 pairs of observations ∑xu = 525, ∑x = 129, ∑ u = 97, ∑x^2 = 687, ∑u^2= 427 and y=10-3u. find the coefficient of correlation between x and y.

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Tejaswi Kasturi (student-cpt) (427 Points)
Replied 25 May 2012

The figures you gave are mathematically impossible. If we try to compute variance for x or u we get negative numbers in the numerator. ∑x = 129 the minimum of ∑x² is when all 20 x are equal i.e x = 129/20 = 6.45 x² = 41.6025 ∑x² = 20*41.6025 = 832.05 check your figures once again. Now I will give the solution for general case

Let ∑x = a , ∑x² = b, ∑u = a₁ , ∑u² = b₁, ∑xu =c

Now y = 10 – 3u ∑y = ∑10 – 3*∑u = 20*10 – 3*a = 200 – 3a₁;

∑y² = ∑(10 – 3u)² = ∑(100 +9u²-60u) = 20*100 +9*b₁-60*a₁ = 2000+9b₁-60a₁

∑xy = ∑x(10 – 3u) = 10∑x – 3∑xu = 10a – 3c

Now correlation between x and y is (N*∑xy – ((∑x)*( ∑y)))/(√(N ∑x² – (∑x)²) * √(N ∑y² – (∑y)²))

= (20*(10a – 3c) - a*(200 – 3a₁))/ (√(20b – (a)²) * √(20(2000+9b₁-60a₁) – (200-3a₁)²))

Substituting the values of a,b,c,a1,b1 we get the correlation

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priya (Student) (64 Points)
Replied 25 May 2012

Thanks for the reply. The question is from the CPT QA book. Hence wanted to know the answer.

intermediate(ipc)course (no) (1460 Points)
Replied 25 May 2012

rxu = Exu/Ex*Eu = 525/129*97=525/12513=0.0420

then y=10-3u

rxy = |-3|*rxu

=3*0.0420

=0.126

Krushna Malu (student) (22 Points)
Replied 17 May 2015

Please help.... ∑xy=414, ∑x=120, ∑y=90 ∑x�=600 ∑y�=300, n=30.later on it was known that two points of observations(12,11) and(6,8)were wrongly taken, the correct pairs of observations being (10,9) and (8,10). The corrected value of correlation is..?

Krushna Malu (student) (22 Points)
Replied 17 May 2015

Sorry....... ∑xy=414, ∑x=120, ∑y=90 ∑x^2 =600, ∑y^2=300, n=30.later on it was known that two points of observations(12,11) and(6,8)were wrongly taken, the correct pairs of observations being (10,9) and (8,10). The corrected value of correlation is..?