statisticalrethinkin..

148 5. MULTIVARIATE LINEAR MODELSkcal.per.g0.5 0.6 0.7 0.8 0.9kcal.per.g0.5 0.6 0.7 0.8 0.955 60 65 70 75neocortex.perc-2 -1 0 1 2 3 4log.masskcal.per.g0.5 0.6 0.7 0.8 0.9kcal.per.g0.5 0.6 0.7 0.8 0.955 60 65 70 75neocortex.perc-2 -1 0 1 2 3 4log.massFIGURE 5.8. Milk energy and neocortex among primates. In the top twoplots, simple bivariate regressions of kilocalories per gram of milk on (le)neocortex percent and (right) log female body mass show weak and uncertainassociations. However, on the bottom, a single regression with bothneocortex percent and log body mass suggests strong association with bothvariables. Both neocortex and body mass are associated with milk energy,but in opposite directions. is masks each variable’s relationship with theoutcome, unless both are considered simultaneously.Now consider another predictor variable, adult female body mass, mass in the dataframe. Let’s use the logarithm of mass, log(mass), as a predictor as well. Why the logarithmof mass instead of the raw mass in kilograms? It is oen true that scaling measurements likebody mass are related by magnitudes to other variables. Taking the log of a measure translatesthe measure into magnitudes. So by using the logarithm of body mass here, we’re sayingthat we suspect that the magnitude of a mother’s body mass is related to milk energy, in alinear fashion.To fit another bivariate regression, with the logarithm of body mass as the predictorvariable now, I recommend transforming mass first to make a new column in the data: