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Name \rule{3in}{0.01in}\\[0.5in]
Email \rule{3in}{0.01in}

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\Large Reading Quiz for Sheather Chapter 7 (Sections 1 \& 2)
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\begin{enumerate}


\item Consider the models M1 and M2:
\begin{eqnarray*}
M1: ~ y & = & X\beta + \epsilon \\ 
M2: ~ y & = & X'\beta' + \epsilon'
\end{eqnarray*}
where $X$ is an $n\times(p_1+1)$ matrix with a column of 1's in the first column, $X'$ is an $n\times(p_2+1)$ matrix with a column of 1's in the first column.
\begin{itemize}
\item Allan took an applied regression class where he learned to use
\[
	AIC_{Allen} = -2\log L(\hat\beta,\hat\sigma^2) + 2(p+2)
\]
\item Alice took a different applied regression class where she learned to use
\[
	AIC_{Alice} = -2\log L(\hat\beta,\hat\sigma^2) + 2p
\]
\end{itemize}
For the purposes of comparing model M1 with model M2, will it make any difference whether we use $AIC_{Allen}$ or $AIC_{Alice}$?  Why or why not?

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\item Suppose we have five regression models, M1, M2, M3, M4 and M5, all five models have the same number of predictors $p$, and they were all fitted on the same data set with $n$ observations.  Suppose RSS is smallest for M4, among all five models.  Mark each statement below as true or false
\begin{enumerate}
\item ~~T~~ or ~~F~~: $R^2$ {\em must} be largest for M4, among these models.
\item ~~T~~ or ~~F~~: $AIC$ {\em must} be smallest for M4, among these models.
\item ~~T~~ or ~~F~~: $BIC$ {\em must} be smallest for M4, among these models.
\end{enumerate}
You do not have to give any explanation or show any work.  Just circle T or F for each statement above.
\end{enumerate}

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