Q59Section I (Objective (Q1–Q80))59 of 80

Linear Models — condition for uncorrelated least squares estimates

Let the model be defined as $\mathbb{E}(Y_1) = 2\beta_1 + \beta_2$ , $\mathbb{E}(Y_2) = \beta_1 - \beta_2$ , $\mathbb{E}(Y_3) = \beta_1 + \alpha\beta_2$ ; where $Y_i$ 's are uncorrelated and have a constant variance $\sigma^2$ . What is the value of $\alpha$ so that the least square estimates of $\beta_1$ and $\beta_2$ are uncorrelated?

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