Least Squares Estimation and ANOVA for Partitioned Models

In the previous chapter, we alluded to the fact that we will eventually use the overall ANOVA to judge whether the variables comprising the model matrix X are, as a whole, important in “explaining” the variation in the elements of y. Often we want to also make this same kind of judgment about groups of explanatory variables or even individual variables. For this and other reasons, we consider in this chapter how the model sum of squares in the overall ANOVA may be partitioned into sums of squares that correspond to the explanatory value of groups of, or individual, variables. We also consider a partition of the residual sum of squares that is possible when multiple observations are taken at one or more combinations of values of the explanatory variables.