Spearman Correlation x=-y

by Fer Stein   Last Updated June 30, 2020 04:19 AM

The exercise consists on proving that if a vector x=-y, then its Spearman correlation is -1. I have tried using the direct formula for the Spearman correlation. However I do not know if all n ranks are distinct integers. Therefore I must employ that $r_s = \frac{cov(rg_X,rg_Y)}{\sigma_(rg_x)\sigma_(rg_y)}$.

I do not know how to proceed

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