Using geographical weighed regression(GWR) model of spatial varying-coefficient regression models(SVCRM) of spatial econometrics,this paper analyses the locally relationship between electricity consumption and economic development of 30 Chinese provinces.

For the linear weighted regression model, this paper defines a new relative effi- ciency, gives it s lower bound and also discusses its relation to other three efficiencies.

The performance comparison among least squares estimate,optimal weighted least squares estimate and linear unbiased minimum variance estimate of column singular design matrix for a linear weighted regression model are presented in this paper.

For the linear weighted regression, lower bounds of four kinds of relative efficiencies of LSE of β (to the BLUE of β ) are given in this paper, and the relation between relative efficiency and generalized coefficient of correlation are built.

The spatial change features of relations between the precipitation on the one hand and longitude,latitude and the altitude above sea level on the other hand are analysed by means of geographically weighted regression and mixed geographically weighted regression.

This paper introduces the global stationary test of regression relation and the stationary test of each regression coefficient changes with spatial location in geographically weighted regression model by theory of least squares estimate.

Based on the data observatory from 216 weather stations in the main land of China from 1961 to 2000,the spatially-varying characteristics of the relationships between the annual precipitation and altitude are analyzed by the geographically weighted regression technique.