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This is a super trivial question, but for some reason I am stuck and I simply don't get what I am missing/doing wrong.

The cosine similarity is defined as followed:

enter image description here

I have this dataset, of points that have their centroid at the origin: enter image description here

I know that the dot product xT * y = 341.575

and I also have both standard deviations

  • std(x) = 9.41
  • std(y) = 8.01

Why is the corr. coeff. p = 0.68?

Why does following term not make sense?
341.75 / (9.41 * 8.01) = 4.53405082117

Anon
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  • Relevant: https://stats.stackexchange.com/questions/235673/is-there-any-relationship-among-cosine-similarity-pearson-correlation-and-z-sc – COOLSerdash Jan 10 '23 at 07:19
  • For $\sqrt{\sum X^2}$ I get $24.91736$ and for $\sqrt{\sum Y^2}$ I get $20.17622$. So the cosine similarity is $341.575/(24.91736\times 20.17622) = 0.679429$ which is very similar (but not exactly identical) to the correlation coefficient. – COOLSerdash Jan 10 '23 at 07:26

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