Question

If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between 2x and y

Answer 1

Correlation coefficient remains unaffected by the change of origin and scale.

i.e., if `"u"_"i" = ("x"_"i" - "a")/"h"` and `"v"_"i" = ("y"_"i" - "b")/"k"`, then Corr (u, v) = ± Corr (x, y), according to the same or opposite signs of h and k.

u_i = `(2("x"_"i" - 0))/1, "v"_"i" = ("y"_"i" - 0)/1`
Here, h = 1 and k = 1 are of the same signs.
∴ Corr (u, v) = Corr (x, y) = 0.8