## 3 Materials and Methods
This shift might reflect a diversification in devices beyond computers, such as smartphones or tablets, suggesting that households are increasingly using various devices for telecommunications rather than relying solely on computers. The correlation between single-service and three-service adoption has also shifted substantially, with the relationship becoming more negative over time, moving from \(-0.18\) in 2015 to \(-0.61\) in 2023. This reflects a clear trend toward multi-service packages as consumers increasingly favor bundled options over isolated, single services. Lastly, the correlation between the adoption of two services and fixed broadband has decreased, moving from 0.90 in 2015 to 0.77 in 2023. This trend may indicate that households are increasingly gravitating toward either single high-quality services or more extensive three-service bundles, with less interest in two-service options. This evolution suggests that consumer preferences may be polarizing towards either minimalist or all-inclusive telecommunications solutions. Figure 4: Correlation matrix of telecommunications data in 2023. Figure 3: Correlation matrix of telecommunications data in 2015. We use the year 2023 as the basis to establish a predictive model regarding fiber optic adoption in households. The methodology continues by loading the dataset containing information on internet access, computer equipment availability, the percentage of households with three telecommunication services, and fiber optic adoption rates across the Mexican states. To facilitate logistic regression, fiber optic adoption is transformed into a binary variable: states with fiber optic adoption rates greater than or equal to 20% are labeled as high adoption (1), while those with rates below 20% are labeled as low adoption (0). A correlation matrix is calculated to explore how the predictor variables--internet access, computer equipment, and three services--relate to each other and to fiber optic adoption. The dataset is then divided into predictor variables (X) and the binary fiber optic adoption target (y). The data are split into training (70%) and testing (30%) subsets, with the training set used to build a logistic regression model. This model estimates the likelihood that a state will adopt fiber optic technology based on its internet access, equipment availability, and services. Cross-validation with five folds is applied to ensure model reliability and reduce overfitting by training and testing the model on different subsets of the data. Finally, predictions for all states are generated, and a bar chart visualizes the predicted probabilities of fiber optic adoption across the Mexican states, highlighting which regions are more likely to adopt advanced technology based on the model's outputs. This method is depicted in Figure 4 with the correlation matrix. In Table 12, \(x1\), \(x2\), and \(x3\) represent the predictor variables used in the logistic regression model to predict fiber optic adoption. \(x1\) refers to broadband access, which indicates the percentage of households with access to broadband internet in each state. \(x2\) corresponds to computer equipment, representing the percentage of households with access to a computer. \(x3\) stands for three services, showing the percentage of households with three fixed telecommunication services (e.g., phone, television, and internet). These predictor variables are used to train the logistic regression model, which aims to forecast whether a state will exhibit high or low adoption of fiber optic technology (the target variable). Each predictor contributes to the model through its respective coefficient, and the model calculates the probability of fiber optic adoption, which is then converted into a binary outcome (0 or 1) to signify low or high adoption. The purpose of these variables is to analyze how internet access, computer availability, and the number of telecommunication services influence the likelihood of fiber optic adoption.