f2009_ex1sol - STA 6207 Exam 1 Fall 2009 PRINT Name...

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Unformatted text preview: STA 6207 Exam 1 Fall 2009 PRINT Name _____________________ All Questions are based on the following 2 regression models, where SIMPLE REGRESSION refers to the case where p =1, and X is of full column rank (no linear dependencies among predictor variables). ( 29 ( 29 I X X Y 2 2 1 1 , ~ 1 ' ' : 2 Model , ~ ,..., 1 : 1 Model N p p n NID n i X X Y i i ip p i i + = = + + + + = Given: ( 29 ( 29 ( 29 ( 29 Y Y Y A AV AY Y A Ax x Ax x' a x x a ' ' symmetric) ( 2 ' + = = = tr E d d d d Cochrans Theorem: Suppose Y is distributed as follows with nonsingular matrix V: ( 29 ( 29 A A Y A Y AV V V Y ' 2 1 : parameter ity Noncentral (b) and ) ( df (a) : with central- non d distribute is 1 ' 1. : idempotent is if n the , ~ 2 2 2 2 = = = r n r N _________________________________________________________________________________________ _ 1. For model 2, derive the least squares estimate for ( 29 ( 29 ( 29 ( 29 ( 29 Y X X X Y X X X X X X Y X X X 2Y Y Y X X X 2Y Y Y X X Y X X Y Y...
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This note was uploaded on 07/28/2011 for the course STA 6208 taught by Professor Park during the Fall '08 term at University of Florida.

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f2009_ex1sol - STA 6207 Exam 1 Fall 2009 PRINT Name...

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