ABSTRACT
The chapter discusses the types of observation that can be made between response variables and explanatory variables. The first distinction depends on the physical character of the measurements and is between extensive and nonextensive variables. The next distinctions depend rather more on the mathematical character of the variable, and in particular on the set of values which it may in principle take. A broad distinction has already been made between descriptive statistics, in which no explicit probabilistic element is involved, and methods in which the idea of probability is central. The method of least squares, which is central to a big part of advanced statistical methods, has various sophisticated probabilistic justifications. Most of another part illustrates methods which have a quite direct probabilistic justification, but it is always important to consider the extent to which the quantities calculated are directly useful as reasonable summaries of the data regardless of the probability model.
