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Math Help - Obtain estimates of b1 and b2 in the regression of Y on X

  1. #1
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    Obtain estimates of b1 and b2 in the regression of Y on X

    How do I solve this question?


    Im aware of B1 and B2 formulas after the OLS derivation, for example B1 = Y + Xbar B2

    But there are no 'x-bar' values in the question. How do i fill them in?
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  2. #2
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    \overline{X} = \frac{\Sigma X_i}{n}

    Let y = b_0 + b_1 x then b_0 = \overline{y} - b_1 \overline{x}

    and b_1 = \frac{\Sigma(X_i - \overline{X})(Y_i - \overline{Y})}{\Sigma(X_i - \overline{X})^2}
    Last edited by statmajor; January 19th 2010 at 08:57 AM.
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  3. #3
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    Be careful with your parenthesis statmajor

    That's essentially the idea though, but you'll have to do some work on \sum (X_i - \bar{X}) ^2 and the like to get something you can work with. In this case it simplifies to \left(\sum X_i ^ 2\right) - n \bar{X} ^ 2.
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  4. #4
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    Quote Originally Posted by theodds View Post
    Be careful with your parenthesis statmajor
    What do you mean by that?
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  5. #5
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    As written, the summation you have in the denominator is identically zero. If you move the parenthesis inside the summation then you are good to go. Although, looking it over again, the numerator needs to be fixed too. Should read \sum (X_i - \bar{X}) (Y_i - \bar{Y})
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  6. #6
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    Thanks for the correction; I'll edit my earlier post.
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