October 20, 2025

Bayesian Method for Linear Regression Modeling; Simulation Study with Normality Assumption

Key Points

The model effectively estimates parameters for independent variables, indicating significant relationships.
Parameter estimates reveal that an increase in one independent variable results in varying impacts on the dependent variable Y.
The model shows good convergence as indicated by the density and trace plots following normal distribution.
With an MSE of 27.17, the model demonstrates strong predictive accuracy relative to data variance.

Abstract

This study aims to conduct regression modeling with parameter estimation using the Bayes method. The Bayes method is an analysis of parameter estimation by looking for solutions from the posterior distribution. The data used are 100 data from simulation results. The prior used is normal prior. The variables used consist of one dependent variable (Y) and three independent variables ( , , dan ) which are normally distributed. A model is obtained that produces significant parameters in all independent variables based on the confidence interval. The interpretation of the model is that if there is a one unit increase in , there will be an increase of 1,950 in Y. If there is a one unit increase in , then Y will decrease by 2,950. If there is a one-unit increase in ( ), there will be an increase of 0.940 in Y. The convergence of parameters is seen from the density plot and trace plot which has followed the normal distribution by looking at the parameters already in the confidence interval. The indicator of model goodness used is MSE. The MSE value obtained is 27.17. The MSE value is relatively small when viewed from the variance and scale of the data. This value proves that this model is good for modeling this case.

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