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If I have the following regression model with intercept $\alpha$ $$y=X\beta + \alpha + \epsilon$$

Is the Weighted Least Squares (WLS) estimator for $\beta$ the same as in the zero-intercept regression?

$$\hat{\beta}=(X'WX)^{-1}X'Wy$$

Which is the WLS estimator for the intercept $\alpha$?

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