Orthogonal Linear Forms in Multivariate Regression Analysis

摘要

A method is developed for the use of orthonormal linear forms in multiple regression analysis. Described in detail are techniques adopted from Hayes and Vickers (Philosophical Magazine, (7) 42,1387) for the solution of the normal equations. These techniques offer the considerable advantages over the standard solutions of being able (a) to select at each stage the variable which makes the maximum contribution to the eventual solution, (b) to decide early in the computations which variables are significant, (c) to permit the deletion of non-significant variables or the addition of new variables (or functions of old ones) without requiring recalculation as would be necessary with standard methods, (d) to give a family of regression curves fitting the data with increasing accuracy so that the regression calculations may be stopped at a stage which has the desired standard error with the minimum number of variables.