## 4 Results and Analysis  
The results below were obtained from the first iteration of data collection sampled across 21 SMEs in Wales back in 2023. It was observed that \"Other--please specify\" was the most common category, with 10 entries, as shown in Figure 4. This suggests that many respondents' industries did not fit into the predefined initial categories declared. \"Engineering, \(\Pi\), and Consultancy\" was the second most common category, with 6 entries. \"Healthcare\" had 3 entries. \"Hospitality and Service\" and \"Insurance\" each had 1 entry. This distribution showed a diverse range of industries in the dataset, with a notable concentration in the \"Other\" category and the \"Engineering, IT, and Consultancy\" sector. The high number of \"Other\" responses indicated that the predefined categories did not fully capture the range of industries represented in the survey. Extracts from results obtained from the second data collection, sampled across 127 SMEs in Wales back in 2023, were also re-examined. The research data here consisted entirely of categorical variables, which resulted in the inability to use traditional regression analysis models that required numerical data. However, this process unlocked valuable insights by transforming these categorical variables into numerical ones. The research used the following Encoding Categorical Variables:  
* One-Hot Encoding: For variables with multiple categories (e.g., color: red, blue, green), the one-hot encoding creates separate binary columns for each category, with a value of 1 indicating membership in that category and 0 otherwise. * Binary Encoding: For yes/no questions, the use of binary encoding, assigning a value of 1 to \"yes\" and 0 to \"no.\"  
Figure 4: Breakdown of the industry variable and its distribution. With the categorical variables encoded, the study addressed the issue of potentially high dimensionality in the data using Dimensionality Reduction. This refers to having a large number of features (variables). Here, the research employed the Principal Component Analysis (PCA). PCA is a technique that reduces the number of dimensions while aiming to capture most of the variance in the data. This simplified analysis and visualization. Once the categorical variables were encoded and PCA performed, the study proceeded with the next steps of analysis. This involved creating a correlation matrix to identify potential relationships between variables and visualizing the data in a lower-dimensional space for better understanding. The results of the correlation matrix for the encoded variables are displayed below in Figure 5:  
The analysis using Principal Component Analysis (PCA) yielded some key observations from Dimensionality Reduction:  
1. Capturing the Big Picture: The first two principal components (PC1 and PC2) managed to explain roughly 50.24% of the total variation present in the original data. By considering the first five principal components, the study captured 100% of the variance. This exploration of these initial components effectively summarizes the most significant patterns within the data. 2. Dissecting Feature Importance: Each original feature contributed differently to the newly formed principal components. For instance, the feature \"Education\" held a greater weight in PC1 and PC3, suggesting its strong influence on the patterns captured by these components. Similarly, \"Age\" was more prominent in PC2, highlighting its significance in a different underlying trend. The table represents the first two principal components extracted from the original data. Each row corresponds to an individual data point (e.g., a survey participant), and the values represent the coordinates of that point in this new, lower-dimensional space created by PCA. Think of PC1 and PC2 as new variables derived from combinations of the original  
Figure 5: Correlation matrix of encoded variables. features. These combinations were chosen to capture the most significant variations in the data.