Independent Variables in Linear Regression Models

This chapter discusses the independent variables in linear regression models. These include the selection of independent variables and stepwise regression, multiple data transformations and polynomial regression, column multicollinearity in design matrix and ridge regression, and recombination of independent variables and principal component regression. The chapter presents some basic principles of univariate and multivariate linear regression. It provides a brief review of the basic statistical results associated with a simple univariate linear regression. The chapter answers for the following questions: what are the principles for selection? How do we choose a good linear regression model? The chapter explains the principal components estimator presented by W.F. Massy. The principal components method is also an appropriate alternative to the ridge regression method in dealing with the problem of multicollinearity. Controlled Vocabulary Terms Fisher’s ztransformation; independent variables; linear regression; polynomial regression; ridge regression; Stepwise multiple regression