Hi,

I have an assignment with part of the question asking me to determine the OLS estimate of Beta given the conditions that

$\displaystyle y = X\beta + u, u $ ~$\displaystyle N(0, \sigma^2I)$

where $\displaystyle X$ is $\displaystyle n x p$ non-stochastic and of rank $\displaystyle p$

I have to take the case $\displaystyle p = 2$ and the matrix X has the form where there are $\displaystyle r$ 1's in the first column with the rest 0's and $\displaystyle s$ 1's in the second column with the rest 0's and with $\displaystyle n = r + s$ (i.e. each row has a 1 and 0 in it, with the 1 in the first column for the first r rows and in the second column for the last s rows).

This leaves the column vector $\displaystyle \beta = (\beta_1, \beta_2)$. As I said I must determine the OLS estimate of $\displaystyle \beta$ in this case. Help?