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\begin{document}
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\begin{flushright}
Name \underline{\hspace{60mm}} \\ 
$\,$ \\
Student Number \underline{\hspace{60mm}}
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\vspace{2mm}

\begin{center}   
{\Large \textbf{STA 431 Quiz 9}}\\
\vspace{1 mm}
\end{center}

\noindent
% \emph{Calculators are allowed.} 

%\vspace{3mm}

\begin{enumerate} 

\item \label{scalarEFA} Let
\begin{eqnarray*}
    z_1 &=& \lambda_1 F_1 +  \lambda_2 F_2 +  \lambda_3 F_3 + e_1 \\
    z_2 &=& \lambda_4 F_1 +  \lambda_5 F_2 +  \lambda_6 F_3 + e_2 
\end{eqnarray*} 
where all expected values are zero, variances of the factors equal one, and all the factors and error terms are independent. As the notation suggests, $Var(z_1) = Var(z_2) = 1$. Only $z_1$ and $z_2$ are observable. Please give Greek letter answers to the following. 
    \begin{enumerate}
        \item (2 points) What is $Var(e_1)$? Show a bit of work. \textbf{Circle your answer.} \vspace{80mm}
        \item (1 point) What is $Corr(z_1, F_3)$? Show a bit of work. \vspace{60mm}
        \item (1 point) What is the reliability of $z_1$ as a measurement of $F_1$? Just write down the answer. \vspace{10mm}

\pagebreak %%%%%%%%%%%%%%%%%%%%%%%%%


        \item (2 points) What is the reliability of $s = z_1 + z_2$ as a measurement of $F_1$? Show your work. \textbf{Circle your answer.} \vspace{120mm}
    \end{enumerate} 
% End scalarEFA



\item \label{R} For the R part of the assignment (last question), you fit a 4-factor model to the \texttt{statclass} data. 
    \begin{enumerate}
        \item (2 points) \label{a} What is the estimated correlation between Factor 2 and mark on Computer Assignment 5? The answer is a number from your printout. \emph{Write the answer in the space below.} Circle the number on your printout, and write ``Q\ref{a}" beside it. \vspace{20mm}
        \item (2 points) \label{b} What estimated proportion of the variance of the Midterm is explained by the common factors? The answer is a number from your printout. \emph{Write the answer in the space below.} Circle the number on your printout, and write ``Q\ref{b}" beside it.
    \end{enumerate} 

\end{enumerate} % End of quiz questions

 \vspace{20mm}
 
\noindent
\textbf{Please attach your printout to the quiz paper. The printout should show your \emph{complete} R input and output.} Make sure your name and student number appear on the printout.

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