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\title{Supplementary Material: A data-driven multiple linear regression model for cardiovascular homeostatic regulation in health, ageing, and disease}

\author[1]{Luis Ruelas, MD}
\author[2]{Claudia Lerma, PhD}
\author[3]{Jesus Espinal, PhD}
\author[4]{Mireya Osorio-Palacios, PhD}
\author[4,5]{Antonio Barajas, PhD}
\author[6]{Bruno Estañol, MD PhD}
\author[4,7]{Ana-Leonor Rivera, PhD}
\author[4,7,*]{Ruben Fossion, PhD}

\affil[1]{Biomedical Sciences PhD Program, National Autonomous University of Mexico (UNAM), Mexico City 04510, Mexico}
\affil[2]{Department of Molecular Biology, National Institute of Cardiology Ignacio Chavez, Mexico City 14080, Mexico}
\affil[3]{National Institute of Genomic Medicine (INMEGEN), Mexico City 14610, Mexico}
\affil[4]{Centre for Complexity Science (C3), National Autonomous University of Mexico (UNAM), Mexico City 04510, Mexico}
\affil[5]{Faculty of Excellence, School of Medicine and Health Sciences, Tecnológico de Monterrey, Monterrey 64700, Mexico}
\affil[6]{National Institute for Medical Sciences and Nutrition Salvador Zubiran, Mexico City 14080, Mexico}
\affil[7]{Institute for Nuclear Science, National Autonomous University of Mexico (UNAM), Mexico City 04510, Mexico}
\affil[*]{Corresponding author: ruben.fossion@nucleares.unam.mx}
\begin{document}
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    \vspace{0.5cm}

    \section*{Normality}

    \begin{table}[ht]
        \centering
        \caption{Results of the Shapiro-Wilk test for the normality of the cardiovascular metrics meanIBI, sdIBI, meanSBP, sdSBP for the individual groups. The null hypothesis is that the data are normally distributed. Statistically significant result imply that the data are not normally distributed  ($p<0.05$, indicated by *).}
        \label{tab:shapiro_wilks}
        \begin{tabular}{|l|l|l|l|l|}
            \hline
            \textbf{Cardiovascular metric} & \textbf{Dataset} & \textbf{Group}          & \textbf{Shapiro-Wilk Statistic} & \textbf{p-value} \\
            \hline
            meanIBI           & AA                  & 18-29y                  & 0.9840                       & $<0.001$ (*)         \\
            &                     & 30-49y                  & 0.9730                       & $0.002$ (*)        \\
            &                     & 50+y                    & 0.9863                       & $0.7007$         \\
            \cline{2-5}
            & T2D                  & Control                 & 0.9508                        & $0.1779$        \\
            &                     & T2D Short-term           & 0.9369                       & $0.0751$         \\
            &                     & T2D Long-term            & 0.9436                       & $0.4293$         \\
            \cline{1-5}
            sdIBI             & AA                  & 18-29y                  & 0.9067                       & $<0.001$ (*)         \\
            &                     & 30-49y                  & 0.9359                       & $<0.001$ (*)         \\
            &                     & 50+y                    & 0.8448                       & $<0.001$  (*)        \\
            \cline{2-5}
            & T2D                  & Control                 & 0.9351                        & $0.0673$         \\
            &                     & T2D Short-term           & 0.9011                       & $0.008$ (*)         \\
            &                     & T2D Long-term            & 0.8088                       & $0.004$ (*)        \\
            \cline{1-5}
            meanSBP           & AA                  & 18-29y                  & 0.9685                       & $<0.001$ (*)        \\
            &                     & 30-49y                  & 0.9787                       & $0.0129$ (*)        \\
            &                     & 50+y                    & 0.9720                       & $0.1538$        \\
            \cline{2-5}
            & T2D                  & Control                 & 0.9772                        & $0.7482$         \\
            &                     & T2D Short-term           & 0.9349                       & $0.0663$         \\
            &                     & T2D Long-term            & 0.9256                       & $0.2344$         \\
            \cline{1-5}
            sdSBP             & AA                  & 18-29y                  & 0.9099                        & $<0.001$ (*)         \\
            &                     & 30-49y                  & 0.8933                       & $<0.001$ (*)        \\
            &                     & 50+y                    & 0.9707                       & $0.1316$         \\
            \cline{2-5}
            & T2D                  & Control                 & 0.9497                        & $0.1663$         \\
            &                     & T2D Short-term           & 0.9184                       & $0.0243$ (*)         \\
            &                     & T2D Long-term            & 0.8517                       & $0.0184$ (*)         \\
            \hline
        \end{tabular}
    \end{table}

    \clearpage

    \section*{Multiple Regression Tables}

    \begin{table}[h!]
        \centering
        \caption{
    Numerical results from the multiple regression analysis of the AA dataset. All models exhibit a variance inflation factor (VIF) below 5, indicating low multicollinearity. For each model, the goodness-of-fit statistic ($R^2$) and the overall p-value are reported. Standardized regression coefficients ($\beta$) and their corresponding $p$-values are provided for each independent variable. Only models meeting both the statistical significance threshold ($p<0.05$) and the explanatory power threshold ($R^2 \geq 0.25$) are included. Independent variables are retained if they satisfy the statistical significance threshold ($p<0.05$), the effect size threshold ($\left| \beta \right| \geq 0.4$), and if the overall model also meets the statistical and explanatory power criteria.
        }
        \label{tab:aa_full_regresions}
        \begin{tabular}{|l|llcc|}
            \hline
            \textbf{Age group}       & \textbf{Dependent variable} & \textbf{Independent variables} & \textbf{$\beta$} & \textbf{$\beta$ (p-value)}\\
            \hline
            \textbf{18-29 years} & \textbf{meanIBI}            & \textbf{sdIBI}                 & $ 0.7767$ (*)     & $<0.001$ (*)                \\
            $n=433$              & $R^2=0.359$ (*)                & meanSBP                        & $-0.0221$      & $0.233$                 \\
            & $p<0.001$ (*)                   & sdSBP                          & $-0.0883$      & $0.026$ (*)                 \\
            \cline{2-5}
            & \textbf{sdIBI}              & \textbf{meanIBI}               & $ 0.5519$ (*)     & $<0.001 (*)$                \\
            & $R^2=0.369$ (*)                & meanSBP                        & $ 0.0205$      & $0.572$                 \\
            & $p<0.001$ (*)                   & sdSBP                          & $ 0.1208$      & $<0.001 (*)$                \\
            \cline{2-5}
            & meanSBP                     & meanIBI                        & $-0.0706$      & $0.233$                 \\
            & $R^2=0.061$                 & sdIBI                          & $ 0.0363$      & $0.572$                 \\
            & $p<0.001$ (*)                   & sdSBP                          & $ 0.2213$      & $<0.001 (*)$                \\
            \cline{2-5}
            & sdSBP                       & meanIBI                        & $-0.1377$      & $0.026$ (*)                \\
            & $R^2=0.085$                 & sdIBI                          & $ 0.2344$      & $<0.001$ (*)                \\
            & $p<0.001$ (*)                   & meanSBP                        & $ 0.2430$      & $<0.001$ (*)                \\
            \hline
            \textbf{30-49 years} & \textbf{meanIBI}            & \textbf{sdIBI}                 & $ 0.7767$ (*)     & $<0.001$ (*)                \\
            $n=163$              & $R^2=0.451$ (*)                & meanSBP                        & $ 0.0221$      & $0.724$                 \\
            & $p<0.001$ (*)                   & sdSBP                          & $-0.1099$      & $0.111$                 \\
            \cline{2-5}   
            & \textbf{sdIBI}              & \textbf{meanIBI}               & $ 0.5772$ (*)     & $<0.001$ (*)                \\
            & $R^2=0.479$ (*)                & meanSBP                        & $-0.0667$      & $0.216$                 \\
            & $p<0.001$ (*)                   & sdSBP                          & $ 0.1884$      & $<0.001$ (*)                \\
            \cline{2-5}
            & meanSBP                     & meanIBI                        & $ 0.0356$      & $0.724$                 \\
            & $R^2=0.035$                 & sdIBI                          & $-0.1443$      & $0.216$                 \\
            & $p=0.128$                   & sdSBP                          & $ 0.1916$      & $0.028$ (*)                 \\
            \cline{2-5}
            & sdSBP                       & meanIBI                        & $-0.1445$      & $0.111$                 \\
            & $R^2=0.087$                 & sdIBI                          & $ 0.3332$      & $0.001$ (*)                \\
            & $p=0.002$ (*)                   & meanSBP                        & $ 0.1567$      & $0.028$ (*)                 \\
            \hline
            \textbf{$>50$ years} & meanIBI                     & sdIBI                          & $ 0.3602$      & $0.004$ (*)                 \\
            $n=64$               & $R^2=0.174$                 & meanSBP                        & $ 0.0229$      & $0.840$                 \\
            & $p=0.008$ (*)                   & sdSBP                          & $-0.3478$      & $0.026$ (*)                 \\
            \cline{2-5}
            & sdIBI                       & meanIBI                        & $ 0.3575$      & $0.004$ (*)                 \\
            & $R^2=0.143$                 & meanSBP                        & $-0.0057$      & $0.959$                 \\
            & $p=0.025$ (*)                   & sdSBP                          & $ 0.2644$      & $0.092$                 \\
            \cline{2-5}
            & meanSBP                     & meanIBI                        & $ 0.0299$      & $0.840$                 \\
            & $R^2=0.003$                 & sdIBI                          & $ 0.0076$      & $0.959$                 \\
            & $p=0.981$                   & sdSBP                          & $-0.0512$      & $0.778$                 \\
            \cline{2-5}
            & sdSBP                       & meanIBI                        & $-0.2304$      & $0.026$ (*)                 \\
            & $R^2=0.083$                 & sdIBI                          & $ 0.1765$      & $0.092$                 \\
            & $p=0.104$                   & meanSBP                        & $-0.0260$      & $0.778$                 \\
            \hline
                \multicolumn{5}{l}{(*) Indicates values and coefficients that comply with a threshold.} \\    
    \multicolumn{5}{l}{\textbf{(boldface)} Indicates models and independent variables that are selected.} \\     
            \end{tabular}
        \label{tab:aa_normotensive_120_cutoff_multiple_regression_all_groups}
    \end{table}

    \clearpage

    \begin{table}[h!]
        \centering
        \caption{
    Numerical results from the multiple regression analysis of the T2D dataset. All models exhibit a variance inflation factor (VIF) below 5, indicating low multicollinearity. For each model, the goodness-of-fit statistic ($R^2$) and the overall p-value are reported. Standardized regression coefficients ($\beta$) and their corresponding $p$-values are provided for each independent variable. Only models meeting both the statistical significance threshold ($p<0.05$) and the explanatory power threshold ($R^2 \geq 0.25$) are included. Independent variables are retained if they satisfy the statistical significance threshold ($p<0.05$), the effect size threshold ($\left| \beta \right| \geq 0.4$), and if the overall model also meets the statistical and explanatory power criteria.
        }
        \label{tab:t2d_full_regresions}
        \begin{tabular}{|l|llcc|}
            \hline
            \textbf{Age group}      & \textbf{Dependent variable} & \textbf{Independent variables} & \textbf{$\beta$} & \textbf{$\beta$ ($p$-value)} \\
            \hline
            \cline{2-5}
            \textbf{non-T2D}        & \textbf{meanIBI}            & \textbf{sdIBI}                 & $ 0.8037$ (*)            & $<0.001$ (*) \\
            $n=30$                  & $R^2=0.425$ (*)                & meanSBP                        & $-0.0274$             & $0.905$ \\
            & $p=0.002$ (*)                   & sdSBP                          & $-0.2885$             & $0.110$ \\
            \cline{2-5}
            & \textbf{sdIBI}              & \textbf{meanIBI}               & $ 0.5082$ (*)            & $<0.001$ (*) \\
            & $R^2=0.502$ (*)                & meanSBP                        & $-0.1466$             & $0.420$ \\
            & $p<0.001$ (*)                   & sdSBP                          & $ 0.3220$             & $0.021$ (*) \\
            \cline{2-5}
            & meanSBP                     & meanIBI                        & $-0.0203$             & $0.905$ \\
            & $R^2=0.062$                 & sdIBI                          & $-0.1718$             & $0.420$ \\
            & $p=0.640$                   & sdSBP                          & $ -0.0231$            & $0.885$ \\
            \cline{2-5}
            & sdSBP                       & meanIBI                        & $-0.3296$             & $0.110$ \\
            & $R^2=0.198$                 & sdIBI                          & $ 0.5817$ (*)             & $0.021$ (*) \\
            & $p=0.120$                   & meanSBP                        & $-0.0357$             & $0.885$ \\
            \hline
            \textbf{Short-term T2D} & meanIBI                     & sdIBI                          & $ 0.1955$             & $0.512$ \\
            $n=30$                  & $R^2=0.047$                 & meanSBP                        & $ 0.0561$             & $0.703$ \\
            & $p=0.732$                   & sdSBP                          & $ 0.0856$             & $0.631$ \\
            \cline{2-5}
            & sdIBI                       & meanIBI                        & $ 0.0855$             & $0.512$ \\
            & $R^2=0.154$                 & meanSBP                        & $-0.0588$             & $0.545$ \\
            & $p=0.218$                   & sdSBP                          & $ 0.2121$             & $0.063$ \\
            \cline{2-5}
            & meanSBP                     & meanIBI                        & $ 0.1012$             & $0.703$ \\
            & $R^2=0.055$                 & sdIBI                          & $-0.2427$             & $0.545$ \\
            & $p=0.680$                   & sdSBP                          & $ 0.2576$             & $0.277$ \\
            \cline{2-5}
            & sdSBP                       & meanIBI                        & $ 0.1053$             & $0.631$ \\
            & $R^2=0.179$                 & sdIBI                          & $ 0.5969$ (*)             & $0.063$ \\
            & $p=0.155$                   & meanSBP                        & $ 0.1756$             & $0.277$ \\
            \hline
            \textbf{Long-term T2D}  & meanIBI                     & sdIBI                          & $ 0.1017$             & $0.735$ \\
            $n=15$                  & $R^2=0.239$                 & meanSBP                        & $ 0.3052$             & $0.228$ \\
            & $p=0.372$                   & sdSBP                          & $ 0.1074$             & $0.706$ \\
            \cline{2-5}
            & sdIBI                       & meanIBI                        & $ 0.1069$             & $0.735$ \\
            & $R^2=0.488$ (*)                 & meanSBP                        & $-0.4353$ (*)             & $0.082$ \\
            & $p=0.054$                  & sdSBP                          & $ 0.6213$ (*)            & $0.015$ (*) \\
            \cline{2-5}
            & meanSBP                     & meanIBI                        & $ 0.4228$ (*)            & $0.228$ \\
            & $R^2=0.409$ (*)                 & sdIBI                          & $-0.5738$ (*)             & $0.082$ \\
            & $p=0.110$                   & sdSBP                          & $ 0.4963$ (*)             & $0.118$ \\
            \cline{2-5}
            & \textbf{sdSBP}              & meanIBI                        & $ 0.1255$             & $0.706$ \\
            & $R^2=0.521$ (*)                & \textbf{sdIBI}                 & $ 0.6908$ (*)            & $0.015$ (*) \\
            & $p=0.040$ (*)                  & meanSBP                        & $ 0.4186$ (*)             & $0.118$ \\
            \hline
                \multicolumn{5}{l}{(*) Indicates values and coefficients that comply with a threshold.} \\    
            \multicolumn{5}{l}{\textbf{(boldface)} Indicates models and independent variables that are selected.} \\    
        \end{tabular}
        \label{tab:dm_120_cutoff_multiple_regression_all_groups}
    \end{table}

    \clearpage

    \setcounter{figure}{0}
    \renewcommand{\thefigure}{S\arabic{figure}}
    \begin{figure}[h!]
        \centering
        
        % Row 1 - Mean NN
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_aa_mean_nn_normal_bp_18-29y.png}
            \label{fig:coef_aa_mean_nn_18_29}
        \end{subfigure}%
        \hfill
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_aa_mean_nn_normal_bp_30-49y.png}
            \label{fig:coef_aa_mean_nn_30_49}
        \end{subfigure}%
        \hfill
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_aa_mean_nn_normal_bp_50+y.png}
            \label{fig:coef_aa_mean_nn_50plus}
        \end{subfigure}
        
        % Row 2 - SD NN
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_aa_sd_nn_normal_bp_18-29y.png}
            \label{fig:coef_aa_sd_nn_18_29}
        \end{subfigure}%
        \hfill
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_aa_sd_nn_normal_bp_30-49y.png}
            \label{fig:coef_aa_sd_nn_30_49}
        \end{subfigure}%
        \hfill
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_aa_sd_nn_normal_bp_50+y.png}
            \label{fig:coef_aa_sd_nn_50plus}
        \end{subfigure}
        
        % Row 3 - Mean SBP
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_aa_mean_sbp_normal_bp_18-29y.png}
            \label{fig:coef_aa_mean_sbp_18_29}
        \end{subfigure}%
        \hfill
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_aa_mean_sbp_normal_bp_30-49y.png}
            \label{fig:coef_aa_mean_sbp_30_49}
        \end{subfigure}%
        \hfill
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_aa_mean_sbp_normal_bp_50+y.png}
            \label{fig:coef_aa_mean_sbp_50plus}
        \end{subfigure}
        
        % Row 4 - SD SBP
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_aa_sd_sbp_normal_bp_18-29y.png}
            \caption*{18-29y}
            \label{fig:coef_aa_sd_sbp_18_29}
        \end{subfigure}%
        \hfill
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_aa_sd_sbp_normal_bp_30-49y.png}
            \caption*{30-49y}
            \label{fig:coef_aa_sd_sbp_30_49}
        \end{subfigure}%
        \hfill
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_aa_sd_sbp_normal_bp_50+y.png}
            \caption*{$>50$y}
            \label{fig:coef_aa_sd_sbp_50plus}
        \end{subfigure}
        
        \caption{Cardiovascular regression models $X_4(X_1,X_2,X_3)$ of eq.~(\ref{regression}) for the AA dataset, for groups 18-29y, 30-49y, and $>50$y (columns), and for the dependent variable $X_4$ corresponding to the cardiovascular metrics meanIBI, sdIBI, meanSBP and sdSBP (rows). Working with standardized regression coefficients allows to represent the contribution of different independent variables $X_1, X_2$ and $X_3$ within the same plot. Indicated are regression models complying with thresholds of statistical significance $p<0.05$ and explanatory power $R^2 \geq 0.25$ (colored background) and independent variables complying with thresholds of statistical significance $p<0.05$ and effect size $\left| \beta \right| \geq 0.4$ (bold line).
        }
        \label{fig:aa_coefficients}
    \end{figure}

    \begin{figure}[h!]
        \centering
        
        % Row 1 - Mean NN
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_bruno_mean_nn_normal_bp_Control.png}
            \label{fig:coef_bruno_mean_nn_control}
        \end{subfigure}%
        \hfill
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_bruno_mean_nn_normal_bp_T2DA.png}
            \label{fig:coef_bruno_mean_nn_t2da}
        \end{subfigure}%
        \hfill
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_bruno_mean_nn_normal_bp_T2DB.png}
            \label{fig:coef_bruno_mean_nn_t2db}
        \end{subfigure}
        
        % Row 2 - SD NN
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_bruno_sd_nn_normal_bp_Control.png}
            \label{fig:coef_bruno_sd_nn_control}
        \end{subfigure}%
        \hfill
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_bruno_sd_nn_normal_bp_T2DA.png}
            \label{fig:coef_bruno_sd_nn_t2da}
        \end{subfigure}%
        \hfill
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_bruno_sd_nn_normal_bp_T2DB.png}
            \label{fig:coef_bruno_sd_nn_t2db}
        \end{subfigure}
        
        % Row 3 - Mean SBP
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_bruno_mean_sbp_normal_bp_Control.png}
            \label{fig:coef_bruno_mean_sbp_control}
        \end{subfigure}%
        \hfill
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_bruno_mean_sbp_normal_bp_T2DA.png}
            \label{fig:coef_bruno_mean_sbp_t2da}
        \end{subfigure}%
        \hfill
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_bruno_mean_sbp_normal_bp_T2DB.png}
            \label{fig:coef_bruno_mean_sbp_t2db}
        \end{subfigure}
        
        % Row 4 - SD SBP
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_bruno_sd_sbp_normal_bp_Control.png}
            \caption*{Non-T2D}
            \label{fig:coef_bruno_sd_sbp_control}
        \end{subfigure}%
        \hfill
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_bruno_sd_sbp_normal_bp_T2DA.png}
            \caption*{Short-term T2D}
            \label{fig:coef_bruno_sd_sbp_t2da}
        \end{subfigure}%
        \hfill
        \begin{subfigure}{0.30\textwidth}
            \centering
            \includegraphics[width=\linewidth]{coef_graph_bruno_sd_sbp_normal_bp_T2DB.png}
            \caption*{Long-term T2D}
            \label{fig:coef_bruno_sd_sbp_t2db}
        \end{subfigure}
        
        \caption{
            Cardiovascular regression models $X_4(X_1,X_2,X_3)$ of eq.~(\ref{regression}) for the T2D dataset, for groups non-T2D, short-term T2D and long-term T2D (columns), and for the dependent variable $X_4$ corresponding to the cardiovascular metrics meanIBI, sdIBI, meanSBP and sdSBP (rows). Working with standardized regression coefficients allows to represent the contribution of different independent variables $X_1, X_2$ and $X_3$ within the same plot. Indicated are regression models complying with thresholds of statistical significance $p<0.05$ and explanatory power $R^2 \geq 0.25$ (colored background) and independent variables complying with thresholds of statistical significance $p<0.05$ and effect size $\left| \beta \right| \geq 0.4$ (bold line).
    %    	Standardized regression relationships among cardiovascular metrics across the T2D dataset groups. Panels are arranged in a 3 × 4 grid, with rows representing the dependent variable: meanIBI, sdIBI, meanSBP, and standard deviation of systolic blood pressure (sdSBP). Columns correspond to groups 18-29y, short-term T2D, and long-term T2D groups. In each panel, the dependent variable (y-axis, standardized units) is modeled as a function of the remaining normalized metrics (x-axis). Colored lines represent regression coefficients with the value of the coefficient being the slope of their respective line. Significant models are represented by a yellow background. Significant coefficients are represented by bold lines.
            }
        \label{fig:bruno_coefficients}
    \end{figure}
\end{document}