THE GENERAL BOX–COX TRANSFORMATIONS IN MULTIPLE LINEAR REGRESSION ANALYSIS

ABSTRACT

A general Box–Cox transformation method in multiple linear regressions is investigated. An algorithm is proposed to identify optimal general Box–Cox transformations based on kernel density estimation techniques. It is shown that for a multiple linear regression problem, the optimal general Box–Cox transformation can be derived through solving a matrix eigenvector problem, while the regression coefficients are estimated by least squares approach. Examples are given to illustrate the proposed method.

Keywords:

• Box–Cox transformation
• Kernel density estimate
• Least squares estimate
• Multiple linear regression

Acknowledgments