ABSTRACT
This chapter deals with computational methods relative to the usual linear model. Two different basic approaches are used for regression computations. One approach is to form the normal equations and proceed with these equations as a starting point. This approach is rejected by some people because it may be very difficult to form the matrices to a high degree of accuracy. The other approach is to avoid formation of the normal equations. Advocates of orthogonalization methods cite their numerical stability and mention that large quantities of storage are available in modern computers at relatively small cost. The chapter deals with use of the normal equations and sweep operations to perform regression analyses. When normal equations form the starting point for regression computations, most algorithms in existence today use sweep operations to solve the system of equations, invert the coefficient matrix, and produce, during the process, several other desired quantities.
