Derive formula of rank correlation
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1. Prove that
2. Using a familiar formula for the sum of the squares of those integers, prove that an expression for for the first n positive integers is
3. If X and Y denote the ranks of an individual with respect to two properties for a group of n individuals, derive the formula for the correlation of the two ranked variables by using the results of problems 1 and 2.
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The expert derives a formula of rank correlation.
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Please see the attached file.
1. Prove that
2. Using a familiar formula for the sum of the squares of those integers, prove that an expression for for the first n positive integers is
3. If X and Y denote the ranks of an individual with respect to two properties for a group of n individuals, derive the formula for the correlation of the two ranked variables by using the results of problems 1 and 2.
1.Problem
_ _
Sx-y ^2 = ___1__∑ {(xi - yi) -( x - y )}^2 , Rearranging the terms we have
n
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= __1__∑ { (xi - x) - ( yi - y ) }^2
n
_ _ _ _ ...
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