## 3 Materials and Methods
The correlation matrices from 2015 and 2023 reveal notable shifts in the relationships between broadband access, telecommunications services, and technology adoption in households. Observing these matrices side by side highlights how advancements in technology, changing consumer behavior, and greater service availability have reshaped the interdependence of these variables. One notable change is in the correlation between fixed broadband access and computer equipment adoption, which has decreased slightly from 0.87 in 2015 to 0.84 in 2023. This suggests that while broadband access and computer equipment remain strongly interdependent, the reliance on broadband for owning computer equipment may have declined slightly as alternative internet access options, such as mobile broadband, have become more prevalent. The relationship between fixed broadband and digital TV also shows a shift, increasing from a correlation of 0.67 in 2015 to 0.78 in 2023. This stronger correlation suggests that digital TV has become more reliant on broadband, likely due to the increasing integration of streaming services, which require stable, high-speed internet. Households may now consider broadband access essential for high-quality, on-demand digital content. An intriguing shift can be seen in the relationship between fixed broadband and the choice of a single service. The correlation has intensified in a negative direction, from \(-0.32\) in 2015 to \(-0.66\) in 2023. This indicates that as broadband access becomes more widespread, households are increasingly opting for multiple telecommunications services rather than relying on a single option. This change suggests a diversification in household service portfolios, likely motivated by the greater availability of bundled services that combine internet, television, and other utilities. A marked shift also appears between fiber optic and cable modem technologies. In 2015, these variables had nearly no correlation (\(-0.03\)), while in 2023, the correlation is more negative (\(-0.53\)), indicating an increasing competition between the two technologies. As fiber optic access has expanded, offering faster and more reliable internet, it has likely begun replacing traditional cable modems in many households, reflecting consumer preference for high-speed internet. Although the correlation between computer equipment and the adoption of three services remains \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline  & **Fixed** & **Computer** & **Digital** & **Fiber** & **Cable** & **One** & **Two** & **Three** \\  & **Broadband** & **Equipment** & **TV** & **Optic**tic & **Modem** & **Service** & **Services** \\ \hline Fixed broadband & 1.000000 & 0.843376 & 0.779258 & 0.488413 & 0.238999 & \(-0.660023\) & 0.774640 & 0.889362 \\ Computer equipment & 0.843376 & 1.000000 & 0.738157 & 0.510704 & 0.249285 & \(-0.541139\) & 0.732809 & 0.809528 \\ Digital TV & 0.779258 & 0.738157 & 1.000000 & 0.472489 & 0.120345 & \(-0.470618\) & 0.690832 & 0.747504 \\ Fiber optic & 0.488413 & 0.510704 & 0.472489 & 1.000000 & \(-0.533534\) & \(-0.385828\) & 0.292593 & 0.503477 \\ Cable modem & 0.238999 & 0.249285 & 0.120345 & \(-0.533534\) & 1.000000 & \(-0.094172\) & 0.353649 & 0.186307 \\ One service & \(-0.660023\) & \(-0.541139\) & \(-0.470618\) & \(-0.358528\) & \(-0.094172\) & 1.000000 & \(-0.418586\) & \(-0.610186\) \\ Two services & 0.774640 & 0.732809 & 0.690832 & 0.292593 & 0.353649 & \(-0.418586\) & 1.000000 & 0.595885 \\ Three services & 0.889362 & 0.809528 & 0.747504 & 0.503477 & 0.186307 & \(-0.610186\) & 0.595885 & 1.000000 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Correlation matrix showing relationships between broadband access, telecommunications services, and technology adoption in households in 2023.  
strong, it has slightly decreased from 0.92 in 2015 to 0.81 in 2023.