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\markboth{36-402: Advanced Data Analysis II {} Spring 1998}{36-402: Advanced Data Analysis II {} Spring 1998}



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\def\class{36-402: Advanced Data Analysis II}

\def\data{\verb|/afs/andrew/stat/data/402|}

\def\term{Spring 1998}

\def\www{{\tt http://www.stat.cmu.edu/\~{}brian/402/}}

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\begin{document}
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\stepcounter{section}
\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{displaymath}Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \beta_3 X_3 + \epsilon
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{tabular}{lr@{$=$}rrr}
\em Source & \multicolumn{2}{c}{\em SS} & 
\multicolumn{1}{c}{\em df} & \multicolumn{1}{c}{\em MS} \\ 
\hline
\\ 
$X_1$            & $SSR(X_1)$         & 17.16 & 1 & 17.16 \\ 
$X_2|X_1$        & $SSR(X_2|X_1)$     & 33.67 & 1 & 33.67 \\ 
$X_3|X_1,X_2$    & $SSR(X_3|X_1,X_2)$ &  3.98 & 1 & 3.98 \\ 
\\ 
\hline
\\ 
Regression & $SSR(X_1,X_2,X_3)$ & 54.80 & 3 & 18.27 \\  
\\ 
\hline
\\ 
Error      & $SSE(X_1,X_2,X_3)$ & 27.67 & $n-4$ = 107 & 0.26 \\ 
\\ 
\hline
\\ 
Total      & $SST$              & 82.47 & $n-1$ = 110 & 
\end{tabular}
}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{displaymath}Y = \beta_0 + \beta_1 X + \epsilon
\end{displaymath}
}

{\newpage
\clearpage
\samepage \psfig{figure=nonlinear.ps,width=6in}
}

{\newpage
\clearpage
\samepage \begin{displaymath}X_1 = \left\{\begin{array}{rr}1 & \mbox{if price$=$\$20.00} \\ 
                              0 & \mbox{else} \end{array}\right.
~~~~~~~~~~~~
X_2 = \left\{\begin{array}{rr}1 & \mbox{if price$=$\$50.00} \\ 
                              0 & \mbox{else} \end{array}\right.
~~~~~~~~~~~~
X_3 = \left\{\begin{array}{rr}1 & \mbox{if price$=$\$90.00} \\ 
                              0 & \mbox{else} \end{array}\right.
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{equation}Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \beta_3 X_3 +
        \epsilon
        \label{naive}
\end{equation}
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{\newpage
\clearpage
\samepage \begin{displaymath}y = \left[
\begin{array}{c}
y_{11} \\ 
y_{21} \\ 
\vdots \\ 
y_{n_11} \\ 
y_{12} \\ 
y_{22} \\ 
\vdots \\ 
y_{n_22} \\ 
y_{13} \\ 
y_{23} \\ 
\vdots \\ 
y_{n_33} 
\end{array}
\right]
= X \beta + \epsilon= 
\left[
\begin{array}{cccc}
1 & 1 & 0 & 0 \\ 
1 & 1 & 0 & 0 \\ 
  & \vdots & & \\ 
1 & 1 & 0 & 0 \\ 
1 & 0 & 1 & 0 \\ 
1 & 0 & 1 & 0 \\ 
  & & \vdots & \\ 
1 & 0 & 1 & 0 \\ 
1 & 0 & 0 & 1 \\ 
1 & 0 & 0 & 1 \\ 
  & & & \vdots  \\ 
1 & 0 & 0 & 1 
\end{array}
\right]
\left[
\begin{array}{c}
\beta_0 \\ 
\beta_1 \\ 
\beta_2 \\ 
\beta_3
\end{array}
\right]
+
\left[
\begin{array}{c}
\epsilon_{11} \\ 
\epsilon_{21} \\ 
\vdots \\ 
\epsilon_{n_11} \\ 
\epsilon_{12} \\ 
\epsilon_{22} \\ 
\vdots \\ 
\epsilon_{n_22} \\ 
\epsilon_{13} \\ 
\epsilon_{23} \\ 
\vdots \\ 
\epsilon_{n_33}
\end{array}
\right]
\end{displaymath}
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\samepage \psfig{figure=plotfactorsales.ps,width=6in}
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{\newpage
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\samepage \begin{displaymath}% latex2html id marker 344
y_{ij} = \mu + \alpha_i + \epsilon_{ij}
\end{displaymath}
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