## 5 Results
### Discussion
#### 5.5.2 Mathematical Modeling and Multidisciplinary Integration  
Concerning the application of the mathematical model, the non-parametric models, which are between one of the many applications in statistics, they allow solving the existing relationships between the variables of interest by using flexible functionalities that approximate unknown relationships between the variables. This entails the need to estimate the density function, where these functions tend to fit the data smoothly, allowing a minimum error to be generated. However, the sample size is also analyzed according to the quantity of the involved random variables. For these aspects, the application of the non-parametric regression model in the current research is considered, establishing the estimates of \(\hat{m}(x)\) of the regression function and an estimator \(\delta^{2}\) of the error variance from the n observations. These procedures of estimation \(m(x)\) are known as smoothed methods \(h\) (bandwidth of the function) of local adjustment, considering only data close to the point where it needs to estimate the function. Therefore, the research focuses on the core function. These core type estimators were designed to solve models with the previously mentioned characteristics.  
Nonetheless, the smoothing parameter estimator \(h\) is fundamental in the appearance and properties of the regression function estimator, where small values of \(h\) generate greater flexibility for the estimator--hence adjusting better to the observed data. At the same time, they may cause high prediction errors, also known as overestimation. However, the high values of \(h\) offer a lower adjustment to the data, but they predict more adequately. If \(h\) is too high, the data being a sub estimation, are not adjusted. Then, depending on the values of \(h\), and the samples for the evaluation of both architectures, the respective analysis between the different variables may be performed.  
At the end of the application of the model, the results allow us to infer that the Monolithic architecture uses 5.47 units less CPU than microservices. In disk reading, they present the same results. In disk writing, however, the Monolithic uses 9.24 units more than microservices. Monolithic uses 1.64 units more than microservices in memory consumption, while the microservices receive 7.2 more units of packages per second compared to the monolithic. Finally, microservices transmit 1.38 packet units per second more compared with a monolithic architecture. The results indicate that the microservices architecture leverages the CPU and packet transmission/reception resources more efficiently compared to the monolithic architecture, which consumes more memory resources and disk writing speed; this would yield a decrease in system performance. Therefore, microservices architecture is an excellent alternative to computer innovation.  
Finally, the application of the non-parametric mathematical procedure, which considers the original data measured in the two analyzed architectures, given the characteristics of its variables, generated greater precision minimizing the error and demonstrating the benefits of the current research.