anonymous
  • anonymous
Could someone tell me how to obtain the least square estimates of the parameters of a regression model? - statistics-
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Are you just looking for linear regression?
anonymous
  • anonymous
yes.only linear regression. generally in term of Y=a+bx+error.
anonymous
  • anonymous
You just want the computation formulas, or theory?

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anonymous
  • anonymous
just want to know how to answer if i got a question like this.
anonymous
  • anonymous
\[b=\frac{\sum(x_i-)(y_i-)}{\sum_{}{}(x_i-)^2}=\frac{s_{xy}}{s_{xx}}\]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:
anonymous
  • anonymous
PS x_i and y_i are data points, , are the means of each.
anonymous
  • anonymous
\[s_{xy}=\sum_{}{}x_iy_i-\frac{\left( \sum_{}{}x_i \right)\left( \sum_{}{}y_i \right)}{n}\]
anonymous
  • anonymous
\[s_{xx}=\sum_{}{}x_i^2-\frac{\left( \sum_{}{}x_i \right)^2}{n}\]
anonymous
  • anonymous
Your intercept, a, can be calculated from\[-b\] where b is the estimate of the slope you would have found from the above.
anonymous
  • anonymous
The process of calculating these wipes epsilon.
anonymous
  • anonymous
You should end up with\[Y=\frac{s_{xy}}{s_{xx}}X+(-b)\]
anonymous
  • anonymous
at this point, what should i do with the equation to get the least square estimation?
anonymous
  • anonymous
Are you talking about epsilon, the error term?
anonymous
  • anonymous
no. i meant for a and b.
anonymous
  • anonymous
Your b is \[b=\frac{s_{xy}}{s_{xx}}\]and your a is\[a=-b\]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.
anonymous
  • anonymous
ok. i understood now.thanks a lot..
anonymous
  • anonymous
No probs. Become a fan ;)

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