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Math Help - Least squares intercept estimator variance

  1. #1
    Newbie Naranja's Avatar
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    Unhappy Least squares intercept estimator variance

    Hello everybody,

    I am tackling the following problem relating to the regression intercept estimator:

    "(a) Show that the least squares estimator \hat{\alpha} = \sum_{i=1}^{n}\Big[\frac{1}{n}-\frac{(x_i-\bar{x})}{S_{xx}}\Big]y_i

    (b) Using the result of part (a), or otherwise, derive the variance of \hat{\alpha}".

    My progress is very limited. On part (a), I cannot see how this is true. Given \hat{\alpha}=\bar{y}-\hat{\beta}\bar{x}, I cannot equate the formula given to what it should be. It seems the formula given amounts to \hat{\alpha}=\bar{y}-\hat{\beta} and I am short of an \bar{x}. I am willing to accept I may have made a mistake but I can't see it and this is a major concern.
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  2. #2
    MHF Contributor
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    Re: Least squares intercept estimator variance

    Hey Naranja.

    Can you show us the complete expanded form by Beta_hat? (i.e. show it in terms of x_i's and y_i's).
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