An algorithm for efficiently generating the design matrix and the associated covarience matrix in linear models

Abstract

is used in the analysis of linear models for estimation, components of variance, and tests of hypothesis is an nxq matrix of zeroes and ones, k q= ~ (ni+l)-i , k being the number of factors, i=l n. being the number of levels of the ith factor, z and R=2k-l. In such situations, the design matrix incorporates information about main effects and their interactions. For example, in a 2x3, factorial experiment, k=2, nl=2 , n2=3 , R=2K-I=3, and