Regression analysis is essential for prediction analysis and variable identification since air pollution studies are complicated by competing suggestions and require careful interpretation. In the existing predictive analysis, estimating indoor radon levels is challenging due to multicollinearity issues and the existing algorithm's assumption of independent predictor variables, making it difficult to accurately assess individual effects. Hence a novel Unsupervised Bayesian Multiple Regression Analysis is used to correctly offer the specific impacts of each predictor variable by taking the complex interactions between factors in the estimation of indoor radon levels. Furthermore, in the variable identification, indoor radon levels are influenced by complex residual distributions, with existing algorithms failing to predict non-Gaussian residuals due to outlier-sensitive least squares estimation. So a novel Quadratic Discriminant Extreme Learning Machine is implemented to overcome this issue, which creates models that are better able to reliably detect the factors driving indoor radon levels and are more robust to non-Gaussian residual distributions. The proposed method demonstrates excellence in predictive analysis and variable identification achieving high coefficient of relation and low MAE.