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414 CHAPTER 16. VARIABLE SELECTION AND MODEL BUILDING

since the parameter interpretations are conditional on which parameters are in
the model.

Note that linear models are rather interpretable to begin with. Later in your
data analysis careers, you will see more complicated models that may fit data
better, but are much harder, if not impossible to interpret. These models aren’t
very useful for explaining a relationship.
To find small and interpretable models, we would use selection criterion that
explicitly penalize larger models, such as AIC and BIC. In this case we still
obtained a somewhat large model, but much smaller than the model we used to
start the selection process.

16.4.1.1 Correlation and Causation

A word of caution when using a model to explain a relationship. There are two
terms often used to describe a relationship between two variables: causation
and correlation. Correlation is often also referred to as association.
Just because two variable are correlated does not necessarily mean that one
causes the other. For example, considering modeling mpg as only a function of
hp.

plot(mpg ~ hp, data = autompg, col = "dodgerblue", pch = 20, cex = 1.5)

40

mpg 30

20

10

50 100 150 200
hp