ABSTRACT
This chapter examines the fundamental computational ideas associated with multiple regression analysis and related computations for the generalized linear model, including the multivariate case. It focuses on particular algorithms only to the extent that they are useful for understanding subsequent computational methods or are helpful in illuminating underlying statistical ideas. The chapter describes one particularly valuable approach to the regression computations, namely, the Householder algorithm, and shall use that algorithm as a starting point from which to compare other algorithms. Most of the standard distributional results from linear models theory can be deduced immediately from the matrix decompositions discussed in this chapter. We assume that the reader is familiar with the linear model, multiple regression analysis, from the statistical and algebraic standpoint. Linear systems such as can be solved using several general methods. The class of methods emphasized up to this point is orthogonalization methods; they operate by transforming the problem into an equivalent, simpler problem by applying orthogonal transformations.
