Question

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

Answer 1

Are you just looking for linear regression?

Answer 2

yes.only linear regression. generally in term of Y=a+bx+error.

Answer 3

You just want the computation formulas, or theory?

Answer 4

just want to know how to answer if i got a question like this.

Answer 5

\[b=\frac{\sum(x_i-<x>)(y_i-<y>)}{\sum_{}{}(x_i-<x>)^2}=\frac{s_{xy}}{s_{xx}}\]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:

Answer 6

PS x_i and y_i are data points, <x>, <y> are the means of each.

Answer 7

\[s_{xy}=\sum_{}{}x_iy_i-\frac{\left( \sum_{}{}x_i \right)\left( \sum_{}{}y_i \right)}{n}\]

Answer 8

\[s_{xx}=\sum_{}{}x_i^2-\frac{\left( \sum_{}{}x_i \right)^2}{n}\]

Answer 9

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.

Answer 10

The process of calculating these wipes epsilon.

Answer 11

You should end up with\[Y=\frac{s_{xy}}{s_{xx}}X+(<y>-b<x>)\]

Answer 12

at this point, what should i do with the equation to get the least square estimation?

Answer 13

Are you talking about epsilon, the error term?

Answer 14

no. i meant for a and b.

Answer 15

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.

Answer 16

ok. i understood now.thanks a lot..

Answer 17

No probs. Become a fan ;)