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Unformatted text preview: Adapted from Vera Tabakova’s notes ECON 6002 Econometrics Memorial University of Newfoundland A.1 Summation A.2 Some Basics A.3 Linear Relationships A.4 Nonlinear Relationships Σ is the capital Greek letter sigma, and means “the sum of.” The letter i is called the index of summation . This letter is arbitrary and may also appear as t , j , or k . The expression is read “the sum of the terms x i , from i equal one to n .” The numbers 1 and n are the lower limit and upper limit of summation. 1 2 1 n i n i x x x x = = + + + ∑ L 1 n i i x = ∑ Rules of summation operation: 1 2 1 n i n i x x x x = = + + + ∑ L 1 1 n n i i i i ax a x = = = ∑ ∑ 1 n i a a a a na = = + + + = ∑ L 1 1 1 ( ) n n n i i i i i i i x y x y = = = + = + ∑ ∑ ∑ 1 1 1 1 1 2 1 1 1 1 1 1 ( ) ( ) n n n i i i i i i i n i i n n n n n n n i i i i i i i i i i i ax by a x b y x x x x x n n x x x x x nx x x = = = = = = = = = = + = + + + + = = = = = = ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ L 1 2 1 ( ) ( ) ( ) ( ) ( ) ("Sum over all values of the index ") ( ) ("Sum over all possible values of ") n i n i i i x f x f x f x f x f x i f x X = = + + + = = ∑ ∑ ∑ L Often you will see an abbreviated 1 1 1 1 1 2 1 1 1 1 1 1 1 ( , ) ( ) ( , ) [ ( , ) ( , ) ( , )] ( , ) ( , ) m n m n i j i j i j i j m n m i j i i i n i j i m n n m i j i j i j j i f x y x y f x y f x y f x y f x y f x y f x y = = = = = = = = = = = = + = + + + = ∑∑ ∑∑ ∑∑ ∑ ∑∑ ∑∑ L Double summation: If f(x,y)=x+y The order of summation does not matter… Product Operator it 1 n t x i t x 1 . x 2 . x 3 .... x n...
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This note was uploaded on 01/26/2011 for the course STAT 2550 taught by Professor Wang during the Spring '10 term at Memorial University.
 Spring '10
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