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 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 = ( 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, = x 2 i y i- n x i y i h n x 2 i- ( x i ) 2 i and 1 = ... h n x 2 i- ( x i ) 2 i Answer 3 y = X + , where y = ( y 1 ,...,y 15 ) , = ( 1 , 2 , 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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L01_easyans - Answers to Exercises in: Review of Elementary...

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