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If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between x-57 and y-38? - Mathematics and Statistics

Sum

If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between `("x" - 5)/7` and `("y" - 3)/8`?

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Solution

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.

Corr `(("x" - 5)/7, ("y" - 3)/8)`= Corr (x, y) = 0.8

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APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 5 Correlation
Miscellaneous Exercise 5 | Q 8. (vi) | Page 64
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