Correlation question

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

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

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

then y=10-3u

rxy = |-3|*rxu

      =3*0.0420

       =0.126