37 Selection of variables under univariate regression models

Abstract

This chapter reviews some methods of selection of variables under univariate regression models. The forward selection, backward elimination and stepwise procedures are discussed in the chapter. These procedures are widely used by many applied statisticians, as computer programs are easily available for their implementation. The chapter discusses some drawbacks of these procedures and the problems of selection of variables within the framework of simultaneous test procedures. The chapter focuses on how the confidence intervals associated with the well known overall F test in regression analysis can be used for the selection of variables. It also discusses some procedures based upon all possible regressions and how the Finite Intersection Tests (FIT) proposed by Krishnaiah for testing the hypotheses on regression coefficients simultaneously can be used for selection of variables. It is known that the FIT is better than the overall F test in terms of the shortness of the lengths of the confidence intervals.