multivariate-statistics/content/introduction.tex

\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}