## 3 Materials and Methods
Additionally, fixed broadband penetration is significantly correlated with the subscription to multiple services, particularly two (0.90) and three services (0.92), indicating that households bundling telecommunication services are more likely to have broadband access. Fiber optic technology, while moderately correlated with fixed broadband (0.68) and multiple services (0.66 for three services), shows growing relevance in regions with more advanced infrastructure but has not yet surpassed older technologies. In contrast, cable modem technology displays weaker correlations with broadband (0.39) and multiple services, suggesting it is less commonly used in areas with modern infrastructure, where fiber optic may be more prevalent. Notably, a negative correlation (\(-0.32\)) between fixed broadband and households with only one service highlights a digital divide, where less technologically equipped households are less likely to have broadband access, underscoring the disparities in service availability and technological adoption. \begin{table}
\begin{tabular}{l l l l l l l l l} \hline  & **Fixed** & **Computer** & **Digital** & **Fiber** & **Cable** & **One** & **Two** & **Three** \\  & **Broadband** & **Equipment** & **TV** & **Optic** & **Modem** & **Service** & **Services** & **Services** \\ \hline Fixed broadband & 1.000000 & 0.871532 & 0.670018 & 0.677981 & 0.386096 & \(-0.321212\) & 0.903438 & 0.921147 \\ Computer equipment & 0.871532 & 1.000000 & 0.686050 & 0.591041 & 0.309805 & \(-0.123736\) & 0.847201 & 0.920141 \\ Digital TV & 0.670018 & 0.686050 & 1.000000 & 0.481157 & 0.232304 & \(-0.000829\) & 0.556294 & 0.739781 \\ Fiber optic & 0.677981 & 0.591041 & 0.481157 & 1.000000 & \(-0.031073\) & \(-0.273230\) & 0.576525 & 0.663063 \\ Cable modem & 0.386096 & 0.309805 & 0.232304 & \(-0.031073\) & 1.000000 & 0.058922 & 0.460581 & 0.246790 \\ One service & \(-0.321212\) & \(-0.123736\) & \(-0.000829\) & \(-0.273230\) & 0.058922 & 1.00000 & \(-0.335279\) & \(-0.183437\) \\ Two services & 0.903438 & 0.847201 & 0.556294 & 0.576525 & 0.460581 & \(-0.325279\) & 1.000000 & 0.773803 \\ Three services & 0.921147 & 0.920141 & 0.739781 & 0.663063 & 0.246790 & \(-0.183437\) & 0.773803 & 1.000000 \\ \hline \end{tabular}
\end{table} 
Table 3: Correlation matrix showing relationships between broadband access, telecommunications services, and technology adoption in households in 2015. The 2016 correlation matrix in Table 4 reveals several important insights into the relationships between broadband access, technological infrastructure, and service adoption in households. A strong correlation between fixed broadband and computer equipment (0.80) highlights that households with greater access to computers are more likely to have broadband connections. Similarly, there is a high correlation (0.91) between fixed broadband and the subscription to three services, indicating that households bundling multiple telecommunications services are more likely to have broadband access, reinforcing the trend of bundled offerings. On the other hand, the correlation between fixed broadband and fiber optic technology is moderate (0.47), suggesting that while fiber optic is associated with advanced infrastructure, its influence is not yet dominant. Interestingly, cable modem technology shows a much weaker correlation with broadband access (0.47) and with other services, reflecting the declining relevance of older technologies in regions with modern infrastructure. The inverse relationship between having only one service and fixed broadband access (\(-0.72\)) indicates that households subscribing to fewer services are less likely to have broadband, signaling a digital divide. The 2017 correlation matrix in Table 5 provides insightful relationships between broadband access, telecommunications services, and technology adoption in households. A strong correlation between fixed broadband and computer equipment (0.87) suggests that households with better access to technology are more likely to adopt broadband services.