Relationship Between BE4DBE2 and Variables n and z: A Comprehensive Analysis Using Linear Regression, Nonparametric Regression, Naive Bayes Classification, Decision Tree Analysis, SVM Analysis, K-Means Clustering, and Bayesian Regression

Abstract

This research employed various statistical techniques, including linear regression, nonparametric regression, Naive Bayes classification, decision tree analysis, Support Vector Machine (SVM) analysis, k-means clustering, and Bayesian regression, to analyze nuclear data. The research aims to explore the relationships between variables, predict binding energy, classify nuclear data, and identify similar groups. The research results revealed that linear regression indicated a significant influence of the intercept and predictor variable 'n' on the variable 'BE4DBE2,' while the variable 'z' was not significant. However, the overall model had limited explanatory power. Nonparametric regression with smoothing functions effectively modeled the relationship between 'BE4DBE2' and variables 'n' and 'z,' explaining approximately 11% of the variability in the response variable. Classification using Naive Bayes successfully categorized nuclear data based on 'n' and 'z,' revealing their relationship. Decision tree analysis evaluated the performance of this classification model and provided insights into accuracy, agreement, sensitivity, specificity, precision, and negative predictive value. SVM analysis successfully built an accurate SVM model with a linear kernel, classifying nuclear data while depicting decision boundaries and support vectors. K-means clustering grouped nuclear data based on 'n' and 'z,' revealing distinct characteristics and enabling the identification of similar clusters. The Bayesian regression model predicted binding energy using 'n' and 'z' as independent variables, capturing the Gaussian distribution of 'BE4DBE2' and providing statistical measures for parameter estimation. Ccomprehensives nuclear data analysis using various statistical approaches provides valuable insights into relationships, predictions, classification, and clustering, contributing to the advancement of nuclear science and facilitating further research in this field.