Linear regression analysis for normal distribution-valued data based on complete information

In light of normal distribution-valued symbolic data, a new method for building linear regression model was proposed. To reflect all the original information of the normal distribution-valued data, definition and calculation principle were proposed for first moments, second original moment and second mixed original moment of normal distribution-valued variables. On this basis, linear regression model for normal distribution-valued data and the sum of squares of the residual information were defined and least-squares regression coefficients were derived. Simulation results show that the explanatory power and predictive ability of the regression model derived by the proposed method are effective and outperform the "Centre Method". The definition and calculation principle of numerical characteristics laid the foundation for extending the other classical multivariate statistical method to distribution-valued data.