Bayesian Regression for Predicting Price Empirical Evidence in American Real Estate

Abstract

The two foremost aims of classical regression are to assess the structure and magnitude of the relationship between variables. Despite the aforementioned benefits, unlike classical regression, which only offers a point estimate and a confidence interval, Bayesian regression offers the whole spectrum of inferential solutions. The results of this study demonstrate the Bayesian approach's suitability for regression tasks and its advantage in accounting for additional a priori data, which often strengthens studies. Using data from Boston Housing provided by from UCI ML Repository, this study proves that the prior distributions have the benefit of producing analytical, closed-form conclusions, which eliminates the need to use numerical techniques like Markov Chain Monte Carlo (MCMC). Second, software implementations are offered together with formulas for the posterior outcomes that are supplied, clarified, and shown. The assumptions supporting the suggested approach are evaluated in the third step using Bayesian tools. Prior elicitation, posterior calculation, and robustness to prior uncertainty and model sufficiency are the three processes that are essential to Bayesian inference.