ABSTRACT
Back in Chapter 1, Section 1, it was explained that the aim of all the work so far is to fit models to a population using data from a sample. The model so fitted shows what values of y are likely to be associated with any given values of the x’ s. Just as any elementary statistics text will warn that a correlation does not imply causation, so a well fitting regression model does not imply that changes in the x values will cause changes in the y variable in accordance the with model. If the model has been constructed by passive observation of sets of y’ s and x’ s, any intervention to change the x values to values which do not occur naturally will change the population to be something different from what the model describes, and so the model no longer applies.
