Fuzzy Statistical Analysis of Multiple Regression with Crisp and Fuzzy Covariates and Applications in Analyzing Economic Data of China

Abstract

This paper extends the simple fuzzy linear regression model to multiple fuzzy linear regression model in which response variable is fuzzy variable and part of the covariates are crisp variables. The least squares methods based on D K -metric and the idea of stepwise regression are applied in parameter estimation. The significance test of the regression coefficients is considered. The Bootstrap methods are used to compute the standard errors of the estimates and P-values of tests. Fuzzy diagnostics based on D K -metric are also developed to detect the outliers. Some simulations are performed to verify the obtained results, which are found to be satisfied. Finally, the early warning of macro-economic index data of China are illustrated our methodology.