An Exploration of Data Prediction Based on Multiple Linear Regression Models and Bayesian Regression

Abstract

In this paper, a hybrid modeling framework integrating multiple linear regression, Bayesian regression and decision tree is proposed for target variable prediction. First, the quantitative prediction of target variables is realized by constructing a multivariate linear regression model with a five-dimensional feature space, and the model is evaluated for performance using F-test and R² value to verify the significance and explanatory power of the combination of independent variables. Secondly, Bayesian regression method is introduced to deal with the binary prediction task, which improves the uncertainty quantification ability through probabilistic modeling and optimizes the feature screening process by combining with the decision tree algorithm, and finally outputs the target breakthrough probability distribution. Finally, the dominant feature dimension is extended to seven dimensions through feature engineering, and the improved model significantly improves the prediction accuracy while maintaining the computational efficiency, which verifies the key role of feature selection on the model performance. The experimental results show that the hybrid model framework has good generalization ability and interpretability in complex prediction scenarios.