sum2 - Summation and Correlation The correlation...

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Unformatted text preview: Summation and Correlation The correlation coefficient r can be written either 1 n n summationdisplay i =1 parenleftBigg ( x i- x ) SD x ( y i- y ) SD y parenrightBigg or parenleftBig 1 n n i =1 x i y i parenrightBig- x y SD x SD y The proof is as follows: 1 n n summationdisplay i =1 parenleftBigg ( x i- x ) SD x ( y i- y ) SD y parenrightBigg = 1 n SD x SD y parenleftBigg n summationdisplay i =1 x i y i- x i y- xy i + x y parenrightBigg = 1 n SD x SD y parenleftBigg n summationdisplay i =1 x i y i- y n summationdisplay i =1 x i- x n summationdisplay i =1 y i + n summationdisplay i =1 x y parenrightBigg = 1 SD x SD y parenleftBigg n i =1 x i y i n- y n i =1 x i n +- x n i =1 y i n + 1 n n summationdisplay i =1 x y parenrightBigg = parenleftBig 1 n n i =1 x i y i parenrightBig- y x- x y + x y SD x SD y = parenleftBig 1 n n i =1 x i y i parenrightBig- x y SD x...
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This note was uploaded on 07/08/2010 for the course STATS 21 taught by Professor Ibser during the Spring '09 term at University of California, Berkeley.

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