\documentclass[11pt]{article} 
%\usepackage{amsbsy} % for \boldsymbol and \pmb 
\usepackage{graphicx} % To include pdf files!
\usepackage{amsmath}
\usepackage{amsbsy}
\usepackage{amsfonts}
%\usepackage[colorlinks=true, pdfstartview=FitV, linkcolor=blue, citecolor=blue, urlcolor=blue]{hyperref} % For links
\usepackage{fullpage}           % Good for US Letter paper

\topmargin=-0.75in
\textheight=9.5in
\usepackage{fancyhdr} 
\renewcommand{\headrulewidth}{0pt}  % Otherwise there's a rule under the header
\setlength{\headheight}{15.2pt}
\fancyhf{}
\pagestyle{fancy} 

\cfoot{Page \thepage {} of 2}
% \pagestyle{empty} % No page numbers


\begin{document}
\enlargethispage*{1000 pt} 

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

\begin{center}   
{\Large \textbf{STA 431 Quiz 7}}\\
\vspace{1 mm}
\end{center}

\noindent
% \emph{Calculators are allowed.} 

%\vspace{3mm}

\begin{enumerate} 

\item In this double measurement path diagram, data for $W_2$ and $Y$ were collected in the same setting and at the same time. They were influenced by common omitted variables, and so their error terms are correlated.  

\begin{center}
\includegraphics[width=3in]{DMsaves}
\end{center}

    \begin{enumerate}
        \item (1 point) Write the model equations. Just write three equations and nothing else. \vspace{35mm}
        \item (1 point) Using the notation $Var(X) = \phi$, $Var(e_1)=\omega_1$, $Var(e_2)=\omega_2$ and $Var(\epsilon) = \psi$, what is the parameter vector $\boldsymbol{\theta}$ for this model? \vspace{30mm}
        \item (1 point) Does this model pass the test of the Parameter Count Rule? Answer Yes or No and give the numbers. \vspace{25mm}

\newpage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

        \item (3 points) Give the covariance matrix of the observable data as a function of the model parameters. Show any necessary calculations. \vspace{120mm}
        \item (2 points) Is the parameter $\beta$ identifiable? If Yes, show it. If No, give two parameter vectors that have \emph{different} values of $\beta$, but produce the same covariance matrix. A simple numerical example would be best. \vspace{35mm}
    \end{enumerate}

\item (2 points) \label{R} For the R part of the assignment, you analyzed the Pig Birth data. In a path diagram of the model (which you do \emph{not} have to give here), there would be a curved double-headed arrow connecting the measurement error terms for Questionnaire One. 

What is the value of the test statistic for testing whether the arrow is present? The answer is a number on your printout. Write the number in the space below. On your printout, circle the number and write ``Question~\ref{R}" beside it. 
\emph{Do not answer this question if you do not have a printout for Question 3 of this weeks's assignment.} \vspace{10mm}

\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.

\end{document}