%  Standard LaTeX document template -- see LaTeX documentation and 
%  manuals for more options and explanations

%  DOCUMENT PREAMBLE

\documentclass[11pt]{article}

%  BE SURE TO PROCESS DOCUMENT TWICE IF IT CONTAINS CROSS-REFERENCES!

%  packages -- here are some examples

\usepackage{fancyheadings}
\usepackage{graphicx,epsf,subfigure}
\usepackage{pstricks,pst-node,psfrag}
\usepackage{amsthm,amssymb,amsmath}

%  some common style parameters appear below; see LaTeX
%  documentation for many others

%  all of these have default values, so if a \setlength
%  declaration does not appear, they are set to the default
%  values

%  values may be in units of inches (in), point (pt, a standard
%  length in printing), em (width of M), or ex (height of x)

\setlength{\oddsidemargin}{0.0in}      % left margin, odd pages
\setlength{\evensidemargin}{0.0in}     % left margin, even pages
\setlength{\topmargin}{-0.01in}        % add to default 1 in
\setlength{\textheight}{9in}           % height of text on page
\setlength{\textwidth}{6.5in}          % widtth of text on page
%\setlength{\parskip}{2.3ex}            % vertical space between paragraphs
%\setlength{\parindent}{0in}            % amount of indentation of paragraph

\renewcommand{\baselinestretch}{1.2}   % changes \baselineskip to
                                       % 1.2 x \baselineskip

%  newcommands -- more newcommands may appear anywhere in the document,
%  not just in the preamble

\newcommand{\bbeta}{\mbox{\boldmath $\beta$}}
\newcommand{\beps}{\mbox{\boldmath $\epsilon$}}
\newcommand{\bX}{\mbox{\boldmath $X$}}
\newcommand{\bY}{\mbox{\boldmath $Y$}}
\newcommand{\bI}{\mbox{\boldmath $I$}}
\newcommand{\N}{\mathcal{N}}

%  MAIN BODY OF DOCUMENT

\begin{document}

%  fooling around with \baselineskip and \baselinestretch allows
%  control over vertical spacing

\setlength{\baselineskip}{0.3in}       % min space from bottom of one line
                                       % to top of next in a paragraph
                                       % place after \begin{document}
              

%  example of sectioning commands with labels for cross-referencing

\section{Introduction}
\label{s:intro}

This is the first paragraph of the document.  This is the first
paragraph of the document.  This is the first paragraph of the
document.  This is the first paragraph of the document.  This is the
first paragraph of the document.  This is the first paragraph of the
document.  This is the first paragraph of the document.

And this is the second paragraph.

\section{Next section}
\label{s:next}

In Section~\ref{s:intro}, we saw that\ldots

\subsection{A subsection}
\label{ss:nextsub1}

Here is some math stuff.  This is the simple linear regression
model for pairs $(x_j,Y_j)$, $j=1,\ldots,n$, with intercept
$\beta_0$ and slope $\beta_1$:
\begin{equation}
Y_j = \beta_0 + \beta_1 x_j + \epsilon_j,
\label{eq:simplelinear}
\end{equation}
where $\epsilon_j$ is a normally-distributed random deviation with
mean 0 and variance $\sigma^2$; that is, 
$$\epsilon_j \sim \N(0,\sigma^2) \hspace{0.1in} \mbox{for all } j.$$

This model can be written alternatively in matrix form.  Let
$$\bY = \left( \begin{array}{c} Y_1 \\ Y_2 \\ \vdots \\ Y_n
\end{array}\right), \hspace{0.1in} \bX = \left( \begin{array}{cc}
1 & x_1 \\ 1 & x_2 \\ \vdots & \vdots \\ 1 & x_n \end{array}
\right),$$ $\bbeta = (\beta_0,\beta_1)^T$, and $\beps =
(\epsilon_1,\epsilon_2,\ldots, \epsilon_n)^T$.  Then
(\ref{eq:simplelinear}) can be expressed more concisely as
\begin{equation}
\bY = \bX \bbeta + \beps.
\label{eq:simplelinear2}
\end{equation}
Thus, (\ref{eq:simplelinear2}) implies that $\bY \sim
\N(\bX\bbeta,\sigma^2 \bI)$, where $\bI$ is an $(n \times n)$ identity
matrix.

\end{document}