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Math Help - slope formula for est. regression equatios

  1. #1
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    slope formula for est. regression equatios

    How is this formula derived

    slope= \frac{\sum(x_{i}-x_{0})(y_{i}-y_{0})}{\sum(x_{i}-x_{0})^2}

    This seems to give me the average ratio of the slope
    \frac{\sum(y_{i}-y_{0})}{\sum(x_{i}-x_{0})}

    I know this is one, but why is it needed?

    \frac{\sum(x_{i}-x_{0})}{\sum(x_{i}-x_{0})}
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  2. #2
    MHF Contributor matheagle's Avatar
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    The x_0 should be \bar x
    and then I really don't understand the second part because

    \sum_{k=1}^n (x_k - \bar x)=0, as well as with the y's.
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  3. #3
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    I'm sorry it should be \frac{x_i-x_o}{x_i-x_o}.
    As far as the x with the bar over it, I just don't know the Latex command for that, so I subbed in the o figuring everyone would understand. I still amm unclear why it is needed. The second part is just a factor I pulled out of the slope equation from above.
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