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Math Help - Pearson Correlation Coefficient Boundary Proof

  1. #1
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    Pearson Correlation Coefficient Boundary Proof

    Given two sequences of numbers x1, .... , xn and y1, ....... , yn,
    the Pearson Correlation Coefficient (PCC) is computed as



    Prove that the -1 <= PCC <= 1, regardless of the values of x and y.


    I do not even know where to start, I know that this correlation is a ratio which tells me to prove the -1 <= PCC <= 1 of any ratio means to prove that denominator >= numerator no matter what values there are.


    Thanks for any guidance/advice
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  2. #2
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    Quote Originally Posted by aaboyd View Post
    Given two sequences of numbers x1, .... , xn and y1, ....... , yn,
    the Pearson Correlation Coefficient (PCC) is computed as



    Prove that the -1 <= PCC <= 1, regardless of the values of x and y.


    I do not even know where to start, I know that this correlation is a ratio which tells me to prove the -1 <= PCC <= 1 of any ratio means to prove that denominator >= numerator no matter what values there are.


    Thanks for any guidance/advice
    It is just the Cauchy-Schwarz inequality.

    CB
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