Uncertain semi-varying coefficient model with application to housing prices

Uncertain regression analysis explores functional relationships in uncertain environments. While existing uncertain statistical models have been widely applied, they often struggle with some complex uncertain phenomena. This paper introduces an uncertain semi-varying coefficient model and derives the parameter vector using the profile least squares method. We provide residual analysis and hypothesis testing to validate the model’s fit, and introduce a significance test for constant coefficients. A case study on house prices demonstrates the model’s effectiveness, highlighting its potential for real-world applications, such as economic forecasting. Statistical tests indicate that the disturbance term should be characterized as an uncertain variable rather than a random one.