# Obtain estimates of b1 and b2 in the regression of Y on X

• Jan 17th 2010, 09:51 AM
Billy Gordon
Obtain estimates of b1 and b2 in the regression of Y on X
How do I solve this question?
http://i50.tinypic.com/vgu5xh.jpg

Im aware of B1 and B2 formulas after the OLS derivation, for example B1 = Y + Xbar B2

But there are no 'x-bar' values in the question. How do i fill them in?
• Jan 17th 2010, 10:41 AM
statmajor
$\displaystyle \overline{X} = \frac{\Sigma X_i}{n}$

Let $\displaystyle y = b_0 + b_1 x$ then $\displaystyle b_0 = \overline{y} - b_1 \overline{x}$

and $\displaystyle b_1 = \frac{\Sigma(X_i - \overline{X})(Y_i - \overline{Y})}{\Sigma(X_i - \overline{X})^2}$
• Jan 19th 2010, 06:26 AM
theodds
Be careful with your parenthesis statmajor :)

That's essentially the idea though, but you'll have to do some work on $\displaystyle \sum (X_i - \bar{X}) ^2$ and the like to get something you can work with. In this case it simplifies to $\displaystyle \left(\sum X_i ^ 2\right) - n \bar{X} ^ 2$.
• Jan 19th 2010, 07:19 AM
statmajor
Quote:

Originally Posted by theodds
Be careful with your parenthesis statmajor :)

What do you mean by that?
• Jan 19th 2010, 07:51 AM
theodds
As written, the summation you have in the denominator is identically zero. If you move the parenthesis inside the summation then you are good to go. Although, looking it over again, the numerator needs to be fixed too. Should read $\displaystyle \sum (X_i - \bar{X}) (Y_i - \bar{Y})$
• Jan 19th 2010, 08:56 AM
statmajor
Thanks for the correction; I'll edit my earlier post.