An Approach for PLS Regression Modeling of Functional Data

Partial Least Squares (PLS) approach is employed for linear regression modeling when both the dependent variables and independent variables are functional data (curves). After the introduction of the constant-style mean, variance and the correlative coefficient of functional data, an approach for PLS regression modeling of functional data is proposed to overcome the multicollinearity existing in the independent variables set. An empirical study of the functional regression modeling shows that the proposed approach provides a tool for building regression model on functional data under the condition of multicollinearity. The empirical study conclusion, which is coincident with the wildly accepted economic theory, indicates that the Compensation of Employees is the most important variable that contributes to the Total Retail Sales of Consumer Goods in China, while the Government Revenue and Income of Enterprises are less important.