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(LSE correlation) Proving that r lies between -1 and 1 watch

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    so I am revising for my statistical theory exam and im my own lecture notes I seem to have put a ('might be in exam') question mark over this issue.

    Economics first year btw.



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    So is L'hopitals rule in order, thats my gut feeling... but how do I do it with sigmas?
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    Are you familiar with the Cauchy-Schwarz inequality? If you define two vectors A and B by A_i = X_i - \bar X and B_i = Y_i = \bar Y, then your fraction is exactly the same as the fraction \dfrac{A \cdot B}{|A||B|}, which has to lie between -1 and 1 since, by the Cauchy-Schwarz inequality, |A \cdot B| \le |A| |B|.
 
 
 

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