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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 8}}\\
\vspace{1 mm}
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\noindent
% \emph{Calculators are allowed.} 

%\vspace{3mm}

\begin{enumerate} 

\item For the following  \emph{scalar} latent variable path diagram,
\begin{center}
\includegraphics[width=3.8in]{LatentPath}
\end{center}

    \begin{enumerate}
        \item (3 points) Write the centered model equations in matrix form as
$\mathbf{y} = \boldsymbol{\beta} \mathbf{y} + \boldsymbol{\Gamma} \mathbf{x} + \boldsymbol{\epsilon}$. The matrices should contain symbols indicated by the path diagram (and zeros).
\vspace{75mm}
        \item (2 points) Give the matrices $\boldsymbol{\Phi}_x = cov(\mathbf{x})$ and $\boldsymbol{\Psi} = cov(\boldsymbol{\epsilon})$. These matrices should contain symbols indicated by the path diagram (and zeros).
\vspace{40mm}
    \end{enumerate}

\item (5 points) \label{R} For the R part of the assignment (last question), you simulated data from a structural equation model and estimated the parameters using \texttt{lavaan}. In the space below, write $\beta_1$ and $\widehat{\beta}_1$. These are numbers from your printout. On the printout, circle and label the numbers.
\vspace{10mm}

%\emph{Do not answer this question if you do not have a printout for Question 9 of this weeks's assignment.} \vspace{7mm}

\end{enumerate} % End of quiz questions

\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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