CHAPTER 12 SimpleLinearRegression

CHAPTER 12 SimpleLinearRegression - G o l d s m a n — I S...

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Unformatted text preview: G o l d s m a n — I S y E 6 7 3 9 L i n e a r R e g r e s s i o n R E G R E S S I O N 1 2 . 1 S i m p l e L i n e a r R e g r e s s i o n M o d e l 1 2 . 2 F i t t i n g t h e R e g r e s s i o n L i n e 1 2 . 3 I n f e r e n c e s o n t h e S l o p e P a r a m e t e r 1 G o l d s m a n — I S y E 6 7 3 9 1 2 . 1 S i m p l e L i n e a r R e g r e s s i o n M o d e l S u p p o s e w e h a v e a d a t a s e t w i t h t h e f o l l o w i n g p a i r e d o b s e r v a t i o n s : ( x 1 , y 1 ) , ( x 2 , y 2 ) , . . . , ( x n , y n ) E x a m p l e : x i = h e i g h t o f p e r s o n i y i = w e i g h t o f p e r s o n i C a n w e m a k e a m o d e l e x p r e s s i n g y i a s a f u n c t i o n o f x i ? 2 G o l d s m a n — I S y E 6 7 3 9 1 2 . 1 S i m p l e L i n e a r R e g r e s s i o n M o d e l E s t i m a t e y i f o r fi x e d x i . L e t ’ s m o d e l t h i s w i t h t h e s i m p l e l i n e a r r e g r e s s i o n e q u a t i o n , y i = β + β 1 x i + ε i , w h e r e β a n d β 1 a r e u n k n o w n c o n s t a n t s a n d t h e e r r o r t e r m s a r e u s u a l l y a s s u m e d t o b e ε 1 , . . . , ε n i i d ∼ N ( , σ 2 ) ⇒ y i ∼ N ( β + β 1 x i , σ 2 ) . 3 G o l d s m a n — I S y E 6 7 3 9 1 2 . 1 S i m p l e L i n e a r R e g r e s s i o n M o d e l y = β + β 1 x w i t h “ h i g h ” σ 2 y = β + β 1 x w i t h “ l o w ” σ 2 4 G o l d s m a n — I S y E 6 7 3 9 1 2 . 1 S i m p l e L i n e a r R e g r e s s i o n M o d e l W a r n i n g ! L o o k a t d a t a b e f o r e y o u fi t a l i n e t o i t : d o e s n ’ t l o o k v e r y l i n e a r ! 5 G o l d s m a n — I S y E 6 7 3 9 1 2 . 1 S i m p l e L i n e a r R e g r e s s i o n M o d e l x i y i P r o d u c t i o n E l e c t r i c U s a g e ( $ m i l l i o n ) ( m i l l i o n k W h ) J a n 4 . 5 2 . 5 F e b 3 . 6 2 . 3 M a r 4 . 3 2 . 5 A p r 5 . 1 2 . 8 M a y 5 . 6 3 ....
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This note was uploaded on 08/27/2011 for the course ISYE 3770 taught by Professor Goldsman during the Spring '07 term at Georgia Tech.

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CHAPTER 12 SimpleLinearRegression - G o l d s m a n — I S...

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