L01_easyans

# L01_easyans - Answers to Exercises in Review of Elementary...

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Unformatted text preview: Answers to Exercises in: Review of Elementary Linear Regression Ideas Stat 640 Answer 1 y 1 y 2 . . . y n = 1 x 1 1 x 2 . . . 1 x n β β 1 ! + 1 2 . . . n . Answer 2 For the two-sample problem we have X X = n 1 n 2 ! , so ( X X )- 1 is easy. The vector X y is simply ( ∑ n 1 i =1 y 1 i , ∑ n 2 i =1 y 2 i ), so that ˆ μ = (¯ y 1 , ¯ y 2 ) . For the simple linear model, X X = n ∑ n i =1 x i ∑ n i =1 x i ∑ n i =1 x 2 i ! , so ( X X )- 1 = ∑ n i =1 x 2 i- ∑ n i =1 x i- ∑ n i =1 x i n ! / n n X i =1 x 2 i- n X i =1 x i ! 2 , Therefore, ˆ β = ∑ x 2 i ∑ y i- n ∑ x i y i h n ∑ x 2 i- ( ∑ x i ) 2 i and ˆ β 1 = ... h n ∑ x 2 i- ( ∑ x i ) 2 i Answer 3 y = Xβ + , where y = ( y 1 ,...,y 15 ) , β = ( β 1 ,β 2 ,β 3 ) , = ( 1 ,..., 15 ) , and X = 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 . Answer 4 For the continuous case, we have simple linear regression:...
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## This note was uploaded on 03/14/2011 for the course STAT 640 taught by Professor Marymeyer during the Spring '08 term at Colorado State.

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L01_easyans - Answers to Exercises in Review of Elementary...

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