ALRLec3 - Chapter 2 Properties of Least Squares (1) As we...

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1 Chapter 2 Properties of Least Squares (1) As we have seen 1 ˆ = SXX SXY = SXX y x n y x i i = SXX y x y x i i i = i i i n i i y c y SXX x x 1 ) ( n i i i n i i y c x y n 1 1 0 1 ˆ = i i n i y x c n ) 1 ( 1 So both 0 ˆ and 1 ˆ are linear combinations of n y y 1 . (2) x ˆ ˆ ) ( ˆ 1 0 x is fitted line Then   y x x x 1 1 ˆ ˆ - y ˆ So fitted least squares line always passes ( x , y ) (3) ) ˆ ˆ ( ˆ 1 0 i i i x y e = 0 ˆ ˆ 1 0 i i x n y (4)       i i i i x c y c 1 0 1 ˆ = i i i x c c 1 0   0 SXX x x c i i
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2   1 SXX SXX SXX x x x x c i i i i Thus   1 1 ˆ       0 1 1 0 1 0 ˆ ˆ ˆ x x x y (5)   1 Var =   i i y c )=   2 2 2 i i i c y c = SXX 2  
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This note was uploaded on 12/12/2010 for the course STAT 425 taught by Professor Ma,p during the Fall '08 term at University of Illinois, Urbana Champaign.

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ALRLec3 - Chapter 2 Properties of Least Squares (1) As we...

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