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Math Help - Easy simple regression model

  1. #1
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    Easy simple regression model

    Let Y_i=\beta_0+\beta_1X_i+\epsilon_i

    I want to show that E[b_0]=\beta_0, where b_0 is an estimate of \beta_0

    b_0=\overline{Y}-b_1\overline{X}

    E[b_0]=E[\overline{Y}]-\overline{X}E[b_1]

    E[b_0]=\beta_0+\overline{X}\beta_1-\overline{X}\beta_1

    E[b_0]=\beta_0

    Is this valid?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by noob mathematician View Post
    Let Y_i=\beta_0+\beta_1X_i+\epsilon_i

    I want to show that E[b_0]=\beta_0, where b_0 is an estimate of \beta_0

    b_0=\overline{Y}-b_1\overline{X}

    E[b_0]=E[\overline{Y}]-\overline{X}E[b_1]

    E[b_0]=\beta_0+\overline{X}\beta_1-\overline{X}\beta_1

    E[b_0]=\beta_0

    Is this valid?
    You have not provided enough context. As it is it looks like you have effectivly assumed the answer, or at least imported other assumptions without telling us what they are.

    You say b_0 is an estimate, but you appear to have a specific extimator in mind.

    CB
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