Question

If the correlation coefficient between X and Y is 0.8, what is the correlation
coefficient between.
(a) X and 3Y
(b) X - 5 and Y - 3

Answer 1

Correlation coefficient does not change in its magnitude under the change of origin and scale.
(i) ∴ r = 0.8 i.e. cor (x, 3y) = cor(x, y) = 0.8

(ii) ∴ r = 0.8 
i.e. cor. (x - 5, y - 3) = cor. (x, y) = 0.8