A New Linear Regression Model and Its Application

Regression analysis is one of the commonly used methods in statistical analysis. However, traditional regression models have less ability for global analysis, and the relationship between variables is often analyzed by methods like the SVD (Singular Value Decomposition), which lack connections with traditional regression analysis. A MGLRM (more generalized linear regression model) is a continuation of traditional linear regression model. In the case that both the predictand and the predictors are scalars, the MGLRM can be transformed into the traditional linear regression model. The MGLRM's basic features include non-commutative multiplication, equivalence to traditional linear regression as predictors in the model are scalars, analysis, extension, dimension-reduction, and robustness, etc. The MGLRM solves problems in traditional linear regression models that have less ability for global analysis and limited expressive ability due to the dimensions of the regression equation. In this paper, the MGLRM and the traditional regression model are applied for statistical analysis of monthly average data of precipitation, height, and wind fields from the NCEP (National Centers for Environmental Prediction) and the western Pacific subtropical high index data from the National Climate Center. Comparison of the results show that the MGLRM has practical implications.