Solution to Tutorial 5 - Tutorial 5 1. Suppose we have n =...

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Unformatted text preview: Tutorial 5 1. Suppose we have n = 10 observations ( X i , Y i ) and fit the data with model Y i = β + β 1 X i + ε i with ε i , i = 1 , ..., 10 are IID N (0 , σ 2 ). We have the following calculations. ¯ X = 0 . 5669 , ¯ Y = 0 . 9624 , n X i =1 Y 2 i = 10 . 2695 , n X i =1 X 2 i = 4 . 0169 , n X i =1 X i Y i = 6 . 2841 . (a) Write down the estimated model b 1 = ∑ n i =1 X i Y i − n ¯ X ¯ Y ∑ n i =1 X 2 i − n ¯ X 2 = 1 . 030974 , b = ¯ Y − b 1 ¯ X = 0 . 3780 SST = n X i =1 ( Y 2 i − ¯ Y ) 2 = n X i =1 Y 2 i − n ¯ Y 2 = 1 . 0069 SSR = b 2 1 n X i =1 ( X 2 i − ¯ X ) 2 = b 2 1 ( n X i =1 X 2 i − n ¯ X 2 ) = 0 . 85427 SSE = SST − SSR = 0 . 15269 , MSE = SSE/ ( n − 2) = 0 . 01908625 Thus s ( b 1 ) = v u u t MSE/ n X i =1 ( X i − ¯ X ) 2 = 0 . 1541026 and s ( b ) = { MSE h 1 n + ¯ X 2 ∑ n i =1 ( X i − ¯ X ) 2 i } 1 / 2 = 0 . 09767 R 2 = SSR/SST = 0 . 8484 , F = SSR/p SSE/ ( n − p − 1) = 44 . 76 , ( with DF = 1 and 8) The model is ˆ Y = 0.37800....
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Solution to Tutorial 5 - Tutorial 5 1. Suppose we have n =...

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