lec27_slides - Review May 7 2019 Linear model I We assume that we are given data Y X where for unit i Yi is the response variable The i-th row of X

# lec27_slides - Review May 7 2019 Linear model I We...

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Review May 7, 2019
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I We showed that 1. If solution is unique then ˆ β = ( X T X ) - 1 X T Y = HY , so ˆ β is a linear estimator. 2. Under the model above the ols estimators satisfies E ( ˆ β ) = β . 3. If in addition, cov ( e ) = σ 2 I , then cov ( ˆ β ) = σ 2 ( X T X ) - 1 . 4. Gauss-Markov theorem. 5. Estimable.
One way ANOVA I Consider the model y ij = μ i + e ij , for i = 1 , . . . , t , and j = 1 , . . . , n i where e ij are i.i.d normal random variables with mean zero and variance σ 2 . Let t i = 1 n i = n .