Laila A. Al-Essa ¹ Endris A. Ebrahim ^2* Yusuf A. Mergiaw ³

• ¹ P.O.Box 84428, Riyadh 11671, Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia
• ² Debre Tabor University, College of Natural and Computational Sciences, Department of Statistics, Applied Statistics, South Gondar, Ethiopia, Addis Ababa, Addis Ababa, Ethiopia
• ³ Department of Mechanical Engineering, Gafat Institute of Technology, Debre Tabor University, Gondar, Amhara, Ethiopia

The majority of research predicted heating demand using linear regression models, but they did not give current building features enough context. Model problems such as Multicollinearity need to be checked and appropriate features must be chosen based on their significance to produce accurate load predictions and inferences. Numerous building energy efficiency features correlate with each other and with heating load in the energy efficiency dataset. The standard Ordinary Least Square regression has a problem when the dataset shows Multicollinearity. Bayesian supervised machine learning is a popular method for parameter estimation and inference when frequentist statistical assumptions fail. The prediction of the heating load as the energy efficiency output with Bayesian inference in multiple regression with a collinearity problem needs careful data analysis. The parameter estimates and hypothesis tests were significantly impacted by the Multicollinearity problem that occurred among the features in the building energy efficiency dataset. This study demonstrated several shrinkage and informative priors on likelihood in the Bayesian framework as alternative solutions or remedies to reduce the collinearity problem in multiple regression analysis. This manuscript tried to model the standard Ordinary Least Square regression and four distinct Bayesian regression models with several prior distributions using the Hamiltonian Monte Carlo algorithm in Bayesian Regression Modeling using Stan and the package used to fit linear models. Several model comparison and assessment methods were used to select the best-fit regression model for the dataset. The Bayesian regression model with weakly informative prior is the best-fitted model compared to the standard Ordinary Least Squares regression and other Bayesian regression models with shrinkage priors for collinear energy efficiency data. The numerical findings of collinearity were checked using variance inflation factor, estimates of regression coefficient and standard errors, and sensitivity of priors and likelihoods. It is suggested that applied research in science, engineering, agriculture, health, and other disciplines needs to check the Multicollinearity effect for regression modeling for better estimation and inference.