Geographically Weighted Regression Model Of Mean Square Error

Geographically weighted regression model puts the nature of spatial data into the regression model, is a improvement of regression models which are in the past. The propose of this model has been widely concerned and applied. Based on the geographical weighted regression model, it is to study the estimated and variance of geographic weighted regression in which the error and variance is not equal, the area of geographic weighted regression model mean square error of the derivation, as well as least squares estimation of the constraint geographical weighted, and give an example of forestry data to establish of forestry tree growth relationship model, and analysis of the general linear regression model which is built and this model.The first paper is the introduction of statistical models, including basic model and nature of the general linear regression model and the estimation of regression parameters, the regression parameter is improved by geographic weighted regression model and be regarded as a function of location on the sample data, applies local parameter estimation method to estimate regression parameter, also describes weighting function selection and bandwidth selection of this model.Thesis is to further theoretical study geographic weighted regression model, let us suppose that the error variances are not equal, it is to study parameter estimation and variance of the corresponding generalized geographically weighted regression. According to the definition of mean square error, derived from the scope of the mean square error of the geographical weighted regression model, according to the relevant theorem, derive from two theorems. Constraints geographical weighted least squares estimation is based on the theory of constrained least squares estimation, on this basis, solved regression parameter estimates and variance of the geographic weighted regression model under binding conditions.The final paper is the part of data analysis and establishment of forestry model, with forestry data as an example, using GWR3.0software to establish the model, analyses this model and the general linear regression model of forestry data. Seen from the table, the GWR model reflects non-stationary nature of the data space. From the point of view, compared with the coefficient of determination and mean square error, GWR model can better detect the relationship of spatial data and fit them.