statisticalrethinkin..

6.1. THE PROBLEM WITH PARAMETERS 177or diet or species age. is is the same “statistical control” strategy explained in the previouschapter.But why use a line to relate body size to brain size? It’s not clear why nature demandsthat the relationship among species be a straight line. Why not consider a curved model,like a parabola? Indeed, why not a cubic function of body size, or even a quintic model? Iagree that there’s no reason yet given to suppose a priori that brain size scales only linearlywith body size. Indeed, many readers will prefer to model a linear relationship between logbrain volume and log body mass (an exponential relationship). But that’s not the directionI’m headed with this example. e lesson here will arise, no matter how we transform thedata. Even aer a log transform of both variables, there’s no reason to insist that linear is theonly imaginable relationship.Let’s fit a series of increasingly complex model families and see which function fits thedata best. We’re going to use lm to fit these models, instead of using map. Take a look back atSection 5.5 (page 166), if you’ve forgotten or missed how these two methods of fitting linearmodels relate to one another. In this case, using lm will get us expediently to the lesson of thissection. We’ll also use polynomial regressions, so review Section 4.5 (page 121) if necessary.e simplest model that relates brain size to body size is the linear one. It will be the firstmodel we consider:v i ∼ Normal(µ i , σ)µ i = α + β 1 m iis is just to say that the average brain volume v i of species i is a linear function of its bodymass m i . Priors are necessarily flat here, since we’re using lm. Now fit this model to the datausing lm:m6.1