multivariate-statistics/content/introduction.tex

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2023-11-16 16:47:14 +01:00
\chapter{Introduction}
\begin{definition}[Long Term Nonprocessor (LTNP)]
Patient who will remain a long time in good health condition, even with a large viral load (cf. HIV).
\end{definition}
\begin{example}[Genotype: Qualitative or Quantitative?]
\[
\text{SNP}:
\begin{cases}
\text{AA} \\
\text{AB} \\
\text{BB}
\end{cases}
\rightarrow
\begin{pmatrix}
0 \\
1 \\
2
\end{pmatrix},
\]
thus we might consider genotype either as a qualitative variable or quantitative variable.
\end{example}
When the variable are quantitative, we use regression, whereas for qualitative variables, we use an analysis of variance.
\begin{figure}
\begin{subfigure}{0.45\columnwidth}
\includegraphics[width=\columnwidth]{figures/plots/linear_regression_linear.pdf}
\end{subfigure}
\begin{subfigure}{0.45\columnwidth}
\includegraphics[width=\columnwidth]{figures/plots/linear_regression_non_linear.pdf}
\end{subfigure}
\caption{Illustration of two models fitting observed values}
\end{figure}