Consider Gauss–Markov linear model as E(Y1)=beta1+beta2, E(Y2)=beta1-alphabeta2, E(Y3)=2beta1-beta2. For what value of alpha, BLUEs of beta1 and beta2 (i.e., hatbeta1 and hatbeta2) are uncorrelated?

Q55Section I (Objective (Q1–Q80))55 of 80

Uncorrelated BLUEs in a Gauss–Markov model

Consider Gauss–Markov linear model as $\mathbb{E}(Y_1)=\beta_1+\beta_2$ , $\mathbb{E}(Y_2)=\beta_1-\alpha\beta_2$ , $\mathbb{E}(Y_3)=2\beta_1-\beta_2$ . For what value of $\alpha$ , BLUEs of $\beta_1$ and $\beta_2$ (i.e., $\hat\beta_1$ and $\hat\beta_2$ ) are uncorrelated?

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