\documentclass[10pt,titlepage,letterpaper,twoside]{book}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{verbatim}
\usepackage{float}
\def\ds{\displaystyle}

\allowdisplaybreaks

\jot=.2in
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\setlength{\textwidth}{7.in}
\font\heada=cmbx10 scaled\magstep3
\font\headb=cmsl10 scaled\magstep1
\font\headc=cmr8
\pretolerance=10000
\raggedright
\setlength{\parindent}{2 em}

\setcounter{MaxMatrixCols}{15}
\setcounter{secnumdepth}{4}
\setcounter{tocdepth}{4}

%\input macros
\def\line#1{\renewcommand{\arraystretch}{#1}}
\def\tab#1{\hspace{.#1in}}
\def\SE{\mathop{S\!E}}
\def\SSR{\mathop{S\!S\!Resid}}
\def\MSR{\mathop{M\!S\!Resid}}
\def\SST{\mathop{S\!S~T\!otal}}
\def\SSTr{\mathop{S\!S~T\!reat}}
\def\MSE{\mathop{M\!S\!E}}
\def\SSE{\mathop{S\!S\!E}}
\def\MSTr{\mathop{M\!S~T\!reat}}
\newcounter{problem}
\newtheorem{thm}{Theorem}
\newsavebox{\mybox}

\newdimen\digitwidth
\newdimen\minuswidth
\setbox0=\hbox{\rm0}
\digitwidth=\wd0
\setbox1=\hbox{$-$}
\minuswidth=\wd1
\newdimen\starr
\setbox2=\hbox{${}^*$}
\starr=\wd2


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\def?{\kern\digitwidth}
\catcode`@=\active
\def@{\kern\minuswidth}
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\def!{\kern\starr}}

\begin{document}
\centerline{\bf EQUATIONS}

{\line3
$$\begin{array}{||c|c|c||}\hline
\ds \bar x = \frac{1}{n}\sum_{i=1}^n x_i &
\ds s^2 = \frac{\ds \sum_{i=1}^n (x_i-\bar x)^2}{n-1} =
\frac{\ds \sum_{i=1}^n x_i^2 - n \bar x^2}{n-1} &
\ds \ds z = \frac{x-\mu}{\sigma_x} \\ \hline\hline
\ds s^2 = \frac{1}{n-1}\left[\sum_{i=1}^n x_i^2 -
  \frac{1}{n}\left(\sum_{i=1}^n x_i\right)^2\right] &
\ds  x_p = \mu + \sigma_x z_p & \ds\sigma_x^2 =
\frac{1}{N}\sum_{i=1}^N(x_i-\mu)^2 \\ \hline P(|X-\mu| \le k\sigma)
\ge 1-\frac{1}{k^2} & \ds\sigma^2_{\bar x} = \frac{\ds
\sigma^2_x}{n}\left(1-\frac{n-1}{N-1}\right) & \ds \sigma^2_{p} =
\frac{\ds\pi(1-\pi)}{n}\left(1-\frac{n-1}{N-1}\right) \\ \hline
\ds\sigma^2_{\bar x} = \frac{\ds \sigma^2_x}{n}  & \ds \sigma^2_{p}
= \frac{\ds\pi(1-\pi)}{n} & \ds n=\frac{\ds
z_{1-\alpha/2}^2\sigma_x^2}{m^2}  \\ \hline \ds n=\frac{\ds
z_{1-\alpha/2}^2\pi(1-\pi)}{m^2} & \ds \bar x \pm
z_{1-\alpha/2}\frac{\ds\sigma_x}{\ds\sqrt{n}} & \ds p \pm
z_{1-\alpha/2}\frac{\ds\sqrt{p(1-p)}}{\ds\sqrt{n}} \\ \hline \ds
\bar x \pm t_{1-\alpha/2,n-1}\frac{\ds s}{\ds\sqrt{n}} & \ds z =
\frac{\ds \bar x - \mu_0}{\ds \sigma_x/\sqrt{n}} & \ds z = \frac{\ds
p - \pi_0}{\ds\sqrt{\pi_0(1-\pi_0)/n}}  \\ \hline \ds t = \frac{\ds
\bar x - \mu_0}{\ds s/\sqrt{n}} & {\line1
\begin{array}{c}\ds \sigma^2_{p_1-p_2} =\\[.2in]
 \frac{\pi_1(1-\pi_1)}{n_1} +
\frac{\pi_2(1-\pi_2)}{n_2}\end{array}} &
{\line1
\begin{array}{c}\ds p_1-p_2 \pm\\[.2in]
z_{1-\alpha/2}\sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2}}\end{array}}
\\ \hline
\ds \sigma^2_{\bar x_1-\bar x_2} = \frac{\sigma_1^2}{n_1} +
\frac{\sigma_2^2}{n_2} &
\ds \bar x_1 -\bar x_2 \pm
t_{1-\alpha/2,d\!f}\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}} &
\ds t=\frac{\bar x_1 - \bar
  x_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2} {n_2}}}  \\ \hline
\ds d\!f = \frac{(V_1+V_2)^2}{\frac{V_1^2}{n_1-1} +
  \frac{V_2^2}{n_2-1}} &
\ds V_1=\frac{s^2_1}{n_1} &
\ds V_2=\frac{s^2_2}{n_2} \\ \hline
\ds z=\frac{\bar x_1 - \bar
  x_2}{\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2} {n_2}}} &
\ds
z=\frac{p_1-p_2}{\sqrt{\frac{p_c(1-p_c)}{n_1}+\frac{p_c(1-p_c)}{n_2}}}
&
\ds p_c = \frac{n_1 p_1 + n_2 p_2}{n_1+n_2} \\ \hline
\ds t=\frac{\bar x_1 - \bar
  x_2}{\sqrt{s_p^2\left(\frac{1}{n_1}+\frac{1}{n_2}\right)}} &
\ds s^2_p = \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2} &
{\line1 \begin{array}{c} \ds \bar x_1 -\bar x_2 \pm \\ \ds
t_{1-\alpha/2,n_1+n_2-2}\sqrt{s_p^2\left(\frac{1}{n_1}+
    \frac{1}{n_2}\right)}\end{array}}\\ \hline
\end{array}$$

\newpage
\label{eqn2}
$$\begin{array}{||c|c|c||}\hline
\ds \bar x_d \pm t_{1-\alpha/2,n-1}\frac{s_d}{\sqrt{n}} &
\ds t = \frac{\bar x_d}{s_d/\sqrt{n}} &
\ds \sigma^2_{\bar x_d} = \frac{\sigma^2_d}{n} \\ \hline
{\line1
\begin{array}{l}\ds X^2 = \sum_{i=1}^k\frac{({\rm obs }_i- {\rm
    expected}_i)^2}{{\rm expected}_i}\\[.1in] df = k-1\end{array}} &
{\line1 \begin{array}{c}\ds \hbox{expected}_i= \ds n \times
\pi_{i_0}
\end{array}}
 &
{\line1
\begin{array}{l}\ds X^2 = \sum_{i=1}^k\frac{({\rm obs }_i- {\rm
    expected}_i)^2}{{\rm expected}_i}\\[.2in]
df=(r-1)(c-1)\end{array}} \\ \hline {\line1 \begin{array}{c} \ds
\hbox{expected}_i= \\ \ds \frac{(\hbox{row total})_i
 \times (\hbox{ col total})_i}{N}\end{array}} &
\ds V^2 = \frac{X^2}{n \times \min(r-1,c-1)} & \ds r =
\frac{1}{n-1}\sum_{i=1}^n\left(\frac{x_i-\bar
x}{s_x}\right)\left(\frac{y_i-\bar y}{s_y}\right)
\\ \hline
\ds y=\beta_0 + \beta_1 x + \epsilon & \ds \hat y = b_0 + b_1 x &
\ds e=y-\hat y \\ \hline \ds \epsilon \sim {\rm N}(0,\sigma) & \ds
\mu_{y|x} = \beta_0 + \beta_1 x & b_1=r\frac{\ds s_y}{\ds s_x}
\\ \hline \ds b_0 = \bar y - b_1 \bar x & \ds SSE=\SSR =
\sum_{i=1}^n e_i^2 & {\line1
\begin{array}{c}
\ds s^2 = MSE= \frac{SSE}{DFE}\\[.1in] DFE=n-2\end{array}} \\ \hline
\ds s^2_y = \frac{SSTo}{n-1} & \ds r^2 = \frac{SSM}{SSTo} &
\sigma_{b_1}^2 = \frac{\ds \sigma^2}{\ds \sum(x_i-\bar x)^2} \\
\hline \ds SE_{b_1} = \sqrt{\frac{\ds MSE}{\sum(x_i-\bar x)^2}} &
\ds b_1 \pm t_{1-\alpha/2,n-2} \times SE_{b_1} & {\line1
\begin{array}{l}\ds t = \frac{b_1}{SE_{b_1}}\\[.1in]
  df=n-2\end{array}}\\ \hline
\ds \hat \mu = b_0+b_1 x^* & \ds SE_{\hat \mu} =
\sqrt{MSE\left(\frac{1}{n}+\frac{(x^*-\bar
    x)^2}{\sum(x_i-\bar
    x)^2}\right)} &
\ds \hat \mu \pm t_{1-\alpha/2,n-2}\times SE_{\hat \mu} \\ \hline
\ds \hat y = b_0+b_1 x^* & \ds SE_{\hat y} = \sqrt{MSE\left(1 +
\frac{1}{n}+\frac{(x^*-\bar
    x)^2}{\sum(x_i-\bar
    x)^2}\right)} &
\ds \hat y \pm t_{1-\alpha/2,n-2}\times SE_{\hat y}\\ \hline  &
\ds x_{ij} = \mu_i + \epsilon_{ij} & \ds  e_{ij}=x_{ij}-\bar x_i
\\ \hline \ds \epsilon_{ij} \sim {\rm N}(0,\sigma)
& \ds SSTo = \sum_{i,~j}(x_{ij}-\bar{\bar x})^2 & \ds \bar{\bar x} =
\frac{1}{N}\sum_{i=1}^k n_i\bar x_i \\ \hline \ds  SSTr =
\sum_{i=1}^k n_i(\bar x_i - \bar{\bar x})^2 & DFTr = k-1 & \ds \SSE
= \sum_{i=1}^k (n_i-1)s^2_i \\ \hline \ds DFE=N-k & \ds F =
\frac{MSTr}{\MSE} & \ds \bar x_i-\bar x_j \pm
q\sqrt{\frac{\MSE}{2}\left(\frac{1}{n_i} + \frac{1}{n_j}\right)}\\
\hline \ds R^2 = \frac{SSTr}{SSTo} & MS = \frac{SS}{DF} & SSTo = SSTr + SSE\\
\hline
DFTo = n-1 & DFTo= DFTr + DFE & \\\hline
\end{array}$$
}
\end{document}