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

Question

anonymous · Answer

Are you just looking for linear regression?

anonymous · Answer

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

anonymous · Answer

You just want the computation formulas, or theory?

anonymous · Answer

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

anonymous · Answer

$$b=\frac{\sum(x_i-)(y_i-)}{\sum_{}{}(x_i-)^2}=\frac{s_{xy}}{s_{xx}}$$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 · Answer

PS x_i and y_i are data points, , are the means of each.

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Your intercept, a, can be calculated from$$-b$$ where b is the estimate of the slope you would have found from the above.

anonymous · Answer

The process of calculating these wipes epsilon.

anonymous · Answer

You should end up with$$Y=\frac{s_{xy}}{s_{xx}}X+(-b)$$

anonymous · Answer

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

anonymous · Answer

Are you talking about epsilon, the error term?

anonymous · Answer

no. i meant for a and b.

anonymous · Answer

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 · Answer

ok. i understood now.thanks a lot..

anonymous · Answer

No probs.  Become a fan ;)