Chapter 8.4 introduces the χ2 distribution and shows how it can be used to assess whether
a model produced by a least-squares fit is consistent with the data. The F distribution, the
distribution of the ratio of two independent random variables that both have χ2 distributions,
is derived. The F distribution and two others derived from it, Student's t distribution and
Hamilton's R-factor ratio distribution, can be used to decide whether one model is
significantly better than another. The projection matrix is defined and the concept of leverage …

In Chapter 8.1, we discussed the method of least squares and procedures for estimating the
values of the adjustable parameters of a model that predicts the mean of a population from
which experimental observations are drawn at random. Any model, however, will have some
set of parameter values that gives the best least-squares® t. We must now address the
question of whether that best® t is adequate, that is, whether it is plausible, given the
precision of the data, to accept the hypothesis that the model really is a correct …