[regression] added note on uniqe parameters

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2020-12-21 14:10:15 +01:00
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5 changed files with 360 additions and 156 deletions

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@@ -28,18 +28,21 @@
\item Move 8.7 to this new chapter.
\item Example that illustrates the Nebenminima Problem (with error
surface). Maybe data generate from $1/x$ and fitted with
$\exp(\lambda x)$ induces local minima.
$c\exp(\lambda x)$ induces local minima.
\item You need initial values for the parameter!
\item Example that fitting gets harder the more parameter you have.
\item Try to fix as many parameters before doing the fit.
\item Ensure that all parameters in the function are unique, e.g. $a e^{x-c} = be^x$.
\item How to test the quality of a fit? Residuals. $\chi^2$ test. Run-test.
\item Impoartant box: summary of fit howtos.
\item Important box: summary of fit howtos.
\end{itemize}
\subsection{New chapter: linear fits --- generalized linear models}
\begin{itemize}
\item Polyfit is easy: unique solution! $c x^3$ is also a linear fit.
\item Example for \emph{overfitting} with polyfit of a high order (=number of data points)
\item Higher order and cross terms
\item Link function, logistic regression
\end{itemize}