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anonymous

  • 5 years ago

Could someone tell me how to obtain the least square estimates of the parameters of a regression model? - statistics-

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  1. anonymous
    • 5 years ago
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    Are you just looking for linear regression?

  2. anonymous
    • 5 years ago
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    yes.only linear regression. generally in term of Y=a+bx+error.

  3. anonymous
    • 5 years ago
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    You just want the computation formulas, or theory?

  4. anonymous
    • 5 years ago
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    just want to know how to answer if i got a question like this.

  5. anonymous
    • 5 years ago
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    \[b=\frac{\sum(x_i-<x>)(y_i-<y>)}{\sum_{}{}(x_i-<x>)^2}=\frac{s_{xy}}{s_{xx}}\]That's what b is BUT, I'm going to give you formulas derived from this that you should use when you want to do any kind of computation:

  6. anonymous
    • 5 years ago
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    PS x_i and y_i are data points, <x>, <y> are the means of each.

  7. anonymous
    • 5 years ago
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    \[s_{xy}=\sum_{}{}x_iy_i-\frac{\left( \sum_{}{}x_i \right)\left( \sum_{}{}y_i \right)}{n}\]

  8. anonymous
    • 5 years ago
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    \[s_{xx}=\sum_{}{}x_i^2-\frac{\left( \sum_{}{}x_i \right)^2}{n}\]

  9. anonymous
    • 5 years ago
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    Your intercept, a, can be calculated from\[<y>-b<x>\] where b is the estimate of the slope you would have found from the above.

  10. anonymous
    • 5 years ago
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    The process of calculating these wipes epsilon.

  11. anonymous
    • 5 years ago
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    You should end up with\[Y=\frac{s_{xy}}{s_{xx}}X+(<y>-b<x>)\]

  12. anonymous
    • 5 years ago
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    at this point, what should i do with the equation to get the least square estimation?

  13. anonymous
    • 5 years ago
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    Are you talking about epsilon, the error term?

  14. anonymous
    • 5 years ago
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    no. i meant for a and b.

  15. anonymous
    • 5 years ago
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    Your b is \[b=\frac{s_{xy}}{s_{xx}}\]and your a is\[a=<y>-b<x>\]You find b first, so you can find a quickly. I didn't put down the sum stuff for a since it would take longer to compute...i.e. you wouldn't use it.

  16. anonymous
    • 5 years ago
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    ok. i understood now.thanks a lot..

  17. anonymous
    • 5 years ago
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    No probs. Become a fan ;)

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