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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
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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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Are you just looking for linear regression?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes.only linear regression. generally in term of Y=a+bx+error.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You just want the computation formulas, or theory?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0just want to know how to answer if i got a question like this.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[b=\frac{\sum(x_i<x>)(y_i<y>)}{\sum_{}{}(x_i<x>)^2}=\frac{s_{xy}}{s_{xx}}\]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:

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0PS x_i and y_i are data points, <x>, <y> are the means of each.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[s_{xy}=\sum_{}{}x_iy_i\frac{\left( \sum_{}{}x_i \right)\left( \sum_{}{}y_i \right)}{n}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[s_{xx}=\sum_{}{}x_i^2\frac{\left( \sum_{}{}x_i \right)^2}{n}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Your intercept, a, can be calculated from\[<y>b<x>\] where b is the estimate of the slope you would have found from the above.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The process of calculating these wipes epsilon.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You should end up with\[Y=\frac{s_{xy}}{s_{xx}}X+(<y>b<x>)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0at this point, what should i do with the equation to get the least square estimation?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Are you talking about epsilon, the error term?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no. i meant for a and b.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Your 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.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok. i understood now.thanks a lot..

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0No probs. Become a fan ;)
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