Question: Show that the log likelihood function for the simple linear regression model is [ -n log sigma-frac{1}{2} sumleft(Y_{u}-beta_{0}-beta_{1} x_{u}ight)^{2} / sigma^{2} ] Deduce that the

Show that the log likelihood function for the simple linear regression model is

\[
-n \log \sigma-\frac{1}{2} \sum\left(Y_{u}-\beta_{0}-\beta_{1} x_{u}ight)^{2} / \sigma^{2}
\]

Deduce that the triple \(\left(\sum Y_{u}, \sum x_{u} Y_{u}, \sum Y_{u}^{2}ight)\) is sufficient for the parameter. Under what conditions is this triple also minimal sufficient?

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