Linear Hypotheses

Abstract

We have seen several examples of hypotheses on models encountered so far. For example, in dealing with polynomial regression §4.1 we met, when dealing with a polynomial model of degree k, the hypothesis that the degree was at most k−1 (that is, that the leading coefficient was zero). In Chapter 5, we encountered nested models, for example two general lines, including two parallel lines. We then met the hypothesis that the slopes were in fact equal (and so the lines were parallel). We can also conduct a statistical check of structural constraints (for instance, that the angles of a triangle sum to two right-angles– see Exercise 6.5).