Thread: deriving the formula for the least square estimates

when deriving the formula for the least squares estimates of veta0 and veta1 from the following population model:

yt=veta0+veta1(xt-xbar)+ut

do you have to do anything different seeing as its normally just Xt not Xt-Xbar.

What im thinking is that you do the normal process for deriving the least sqaure estimates, however wasnt sure because of the Xt minus Xbar

also I dont know how to insert symbols and formula hence what I have written, I hope its understandable

Originally Posted by nickpatto

when deriving the formula for the least squares estimates of veta0 and veta1 from the following population model:

yt=veta0+veta1(xt-xbar)+ut

do you have to do anything different seeing as its normally just Xt not Xt-Xbar.

What im thinking is that you do the normal process for deriving the least sqaure estimates, however wasnt sure because of the Xt minus Xbar

also I dont know how to insert symbols and formula hence what I have written, I hope its understandable

Rewrite your model as:

yt=veta1*xt+c+ut

with c=veta0-veta1*xbar, now do the regression.

CB

Hi thanks for that but I need to derive the formula for the estimates veta0 and veta1.

The normal formula when the regression is Yi=veta0+veta1Xi+ui is the following:

the intercept estimate (veta0) is

veta0=Ybar-veta1xbar

and the slope intercept (veta1)

veta1= sum of(xi-xbar)(yi-ybar)/sum of (xi-xbar)squared

Whats confusing me is that the regression model i have been given is

yt=veta0+veta1(xt-xbar)+ut

the fact that its not just Xi after veta1 is confusing me, I dont know if i can just use the formulas for the estimates that i used about or because its xt-xbar do i need to do something different when deriving my forumlas for my estimates?