ALRLec5 - 1 CHAPTER 3: MULTIPLE REGRESSION Multiple Linear...

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Unformatted text preview: 1 CHAPTER 3: MULTIPLE REGRESSION Multiple Linear Regression Response: Y Predictors: p X X X ,..., , 2 1 Multiple linear regression model: 2 1 1 1 1 1 1 ] ,..., | [ ... ] ,..., | [ = = = + + + = = = p p p p p p x X x X Y Var x x x X x X Y E 2 1 ,..., , and p are unknown parameters. Alternatively, we can write above model as following: e x x Y p p + + + + = ... 1 1 With n observations we have: t independen e e Var e E e x x y i i i i ip p i i 2 1 1 ] [ ] [ ... = = + + + + = Writing as vector form, we have: i T i i e x y + = [ ] = = = p ip i i T i ip i i i x x x x x x x x . . . ..... 1 . . . 1 2 1 2 1 2 1 2 Writing as matrix form: ) 1 ( ) 1 ( ) 1 ( 1 nx xn p p nx nx e X Y + = + +...
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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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ALRLec5 - 1 CHAPTER 3: MULTIPLE REGRESSION Multiple Linear...

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