Nonlinear Depreciation and Brand Heterogeneity in Chinese Used-Car Listing Prices: An Interpretable Hedonic Regression and Out-of-Sample Evaluation

Using 1,000 used-car listings obtained through a CSDN community competition, this study examines whether an interpretable hedonic specification can describe nonlinear age–price relationships, luxury-brand heterogeneity, and held-out predictive performance. The sample is randomly divided into 800 training and 200 test observations. Three nested log-linear ordinary least squares (OLS) specifications are estimated: a baseline model, a model with squared mean-centred age, and a full model that also includes a luxury-brand × mean-centred-age interaction. In the final specification, the conditional association between age and log listing price is negative at the sample mean and becomes less negative as age increases; the luxury-brand age interaction is also negative. Orthogonalized log mileage is not statistically significant once the nonlinear age terms and observed controls are included. On the held-out test set, Model C records RMSE 1.569, MAE 1.088, and MAPE 10.23% (price is measured in ten-thousand yuan). These results are descriptive and predictive within the observed listing sample; they do not establish causal depreciation effects or general superiority over alternative algorithms.