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# tutorial 5 - Tutorial 5 1 Suppose we have n = 10...

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Tutorial 5 1. Suppose we have n = 10 observations ( X i , Y i ) and fit the data with model Y i = β 0 + 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 i =1 Y 2 i = 10 . 2695 , n i =1 X 2 i = 4 . 0169 , n i =1 X i Y i = 6 . 2841 . (a) Write down the estimated model (b) Test H 0 : β 1 = 1 with α = 0 . 05 (c) For a new X = 1, find the 95% CI for its expected response (d) For a new X = 0 . 5, find the 95% prediction interval for its possible response 2. For the least square estimator b 0 , b 1 of simple linear regression model, find Cov ( b 0 , b 1 ) 3. Suppose A : m × n is a constant matrix and Y : n × 1 , is a random vector. Then Var ( AY ) = A Var ( Y ) A Please give your proof for m = 2

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tutorial 5 - Tutorial 5 1 Suppose we have n = 10...

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