========
  Teil 1
 ========

\begin{exampl}[Profile computation] \begin{comment}EXCLUDE\end{comment} Suppose
taxonomy $C$ as depicted in Figure \ref{small-taxo}, and propagation
factor $\kappa=1$. Let $a_{i}$ have implicitly rated four books, namely Matrix Analysis,
Fermat's Enigma, Snow Crash, and Neuromancer. For Matrix Analysis,
five topic descriptors are given, one of them pointing to leaf
topic \textsc{Algebra} within our small taxonomy.

Suppose that $s = 1000$ defines the overall accorded profile
score. Then the score assigned to descriptor \textsc{Algebra}
amounts to $s\,/\,(4 \cdot 5) = 50$. Ancestors of leaf
\textsc{Algebra} are \textsc{Pure}, \textsc{Mathematics},
\textsc{Science}, and top element \textsc{Books}. Therefore, score
$50$ must be distributed among these topics according to Equation
\ref{PG-2} and \ref{PG-3}. The application of Equation \ref{PG-4}
yields score $29.091$ for topic \textsc{Algebra}. Likewise,
applying Equation \ref{PG-3}, we get $14.545$ for topic
\textsc{Pure}, $4.848$ for \textsc{Mathematics}, $1.212$ for
\textsc{Science}, and $0.303$ for top element \textsc{Books}.
These values are then used to build profile vector $\vec{v_{i'}}$ of $a_{i}$.
\end{exampl}

...

Analyzing multiple linear regression results, shown in Table
\ref{MLR}, confidence values $P(>|t|)$ clearly indicate that
statistically significant correlations for accuracy and covered
range with user satisfaction exist.
Since statistical significance also holds for their respective
second-order polynomials, i.e., CR$^{2}$ and SVA$^{2}$, we
conclude that these relationships are non-linear and more complex,
though.

As a matter of fact, linear regression delivers a strong
indication that the intrinsic utility of a list of recommended
items is more than just the average value of accuracy votes for
all single items, but also depends on the perceived diversity.

...

\begin{tabular}{lcccc}
& \textbf{Estimate} & \textbf{Error} & \textbf{$t$-Value} & \textbf{$P(>|t|)$}\\[2ex]
\textbf{(const)} & 3.27 &  0.023 & 139.56 & $< 2e-16$ \\[2ex]
SVA & 12.42 &  0.973 & 12.78 & $< 2e-16$ \\
SVA$^{2}$ & -6.11 & 0.976 & -6.26 & $-4.76e-10$ \\[2ex]
CR & 19.19 & 0.982 & 19.54 & $< 2e-16$ \\
CR$^{2}$ & -3.27 & 0.966 & -3.39 & \ $0.000727$ \\ \\[-1ex]
%\hline \\[-1ex]begin
\multicolumn{5}{r}{Multiple $R^{2}$: 0.305, adjusted $R^{2}$: 0.303}\\[2ex]
\begin{comment}INCLUDE\end{comment}\end{tabular}