Land subsidence caused by groundwater overexploitation is a critical global problem. Spatial distribution of land subsidence is crucial for environmental management and land planning due to the sensitive nature of land-surface gradients. Given the nonlinear relationship of subsidence and long-term drawdown from groundwater exploitation, and the heterogeneity of the aquifer in the Choshui River alluvial fan, a developed spatial regression model can effectively estimate nonlinear and spatially varying subsidence. That is, the root-mean-square-errors (RMSEs) of annual subsidences are less or equal to 0.8 cm. Considering various data inputs in the Choshui River alluvial fan, the spatial regression model offers a robust method for estimating the spatial patterns of subsidence using drawdown as observations. Results show that the largest water-level cone of depression occurs in the distal fan area. Nonetheless, the calculated subsidence bowl closely approximates the observed one located much farther inland. Without requiring extensive calibration or an elaborate numerical groundwater flow and subsidence model, the model provides reasonable and detailed patterns using a spatially varying relationship between drawdown and resulting land subsidence. Results indicate that the spatial regression model reasonably estimates the spatial distribution of the skeletal storage coefficient in the aquifer system. The large coefficient that represents inelastic compaction occurs in the inland areas, whereas the small coefficient that represents elastic compaction occurs along the coastal area. Furthermore, this model is relevant for water policy or land subsidence regulation.