Note on Second‐Order Polynomial Regression Models
这篇短文针对多项式回归模型中严重的多重共线性问题，提出一种简单变换，使线性项与二次项正交，从而消除共线性，并用实例展示了该方法的优势。
ABSTRACT Polynomial regression models have applications in the social sciences and in business research. Unfortunately, such models have a high degree of multicollinearity that creates problems with the statistical assessment of the model. In fact, the collinearity may be so severe that it could lead to an incorrect conclusion that some of the terms in the model are not statistically significant and should therefore be omitted from the model. This note provides a simple transformation to achieve orthogonality in polynomial models between the linear and quadratic terms, thereby eliminating the collinearity problem. It also shows that the same procedure does not achieve orthogonality for higher‐order terms. An example data set is analyzed to show the benefits of such a procedure.