Abstract
An administrative district is considered a fuzzy set with respect to physical environment. For example, a multiple regression equation for predicting rice yield in Fukushima prefecture should be somewhat applicable to data in Ibaraki prefecture, a neighboring district. This principle yields the weighted least squares, which makes a multiple linear equation effective in predicting rice yield in both Fukushima and Ibaraki. Optimization of the weight using cross-validation substantially enhances the predictability of multiple regression. This method is associated with bias regression such as smoothing spline and ridge regression. However, there are some open problems : definition of fuzzy set in this methodology and applicatino to nonlinear regressino such as neural network.
