Past exam of the options I course of the University of Oxford / 2010 / O / O2 / a

Full column rank gives the least-squares estimatorWrite $A=(X^{T}X{)}^{-1}{X}^T$. Since $AX=I$ and $\mathrm{Cov}(ϵ)={\sigma }^{2}I$, we have $\hat{\theta }=\theta +Aϵ$ andThis calculation needs the stated uncorrelated equal-variance errors, but not normality.