statisticalrethinkin..

5.3. WHEN ADDING VARIABLES HURTS 153bl -0.06 1.94 -3.87 3.75br 2.11 1.96 -1.72 5.94sigma 0.57 0.04 0.49 0.65ose posterior means and standard deviations look crazy. is is a case in which a graphicalview of the precis output is more useful, because it displays the posterior means and 95%intervals in a way that allows us with a glance to see that something has gone wrong here:plot(precis(m5.8))R code5.30ablbrsigma-4 -2 0 2 4 6EstimateYour numbers and precis plot will not look exactly the same, due to simulation variance.But they will show the same odd result. If both legs have almost identical lengths, and heightis so strongly associated with leg length, then why is this posterior distribution so weird? Didthe model fitting work correctly?e model did fit correctly, and the posterior distribution here is the right answer tothe question we asked. Recall that a multiple linear regression answers the question: whatis the value of knowing each predictor, aer already knowing all of the other predictors? So inthis case, the question becomes: what is the value of knowing each leg’s length, aer alreadyknowing the other leg’s length?e answer to this weird question is equally weird, but perfectly logical. e posteriordistribution is the answer to this question, considering every possible combination of theparameters and assigning relative plausibilities to every combination, conditional on thismodel and these data. It might help to look at the bivariate posterior distribution for bl andbr:post