Using R for Introductory Statistics : John Verzani

Bivariate data 93■ Example 3.6: Kids’ weights: Is weight related to height squared?In Figure 3.8, the relationship between height and weight is given for the kid. weights(UsingR) data set. In Example 3.4, we mentioned that the BMI suggests a relationshipbetween height squared and weight. We model this as follows:> height.sq = kid.weights$height^2> plot(weight ~ height.sq, data=kid.weights)> res = 1m(weight ~ height.sq, data=kid.weights)> abline(res)> resCall:1m(formula = weight ~ height.sq, data=kid.weights)Coefficients:(Intercept) height.sq3.1089 0.0244Figure 3.12 Height squared versusweightFigure 3.12 shows a better fit with a linear model than before. However, the BMI is notconstant during a person’s growth years, so this is not exactly the expected relationship.Using a model formula with transformations If we had tried the above exampleusing this model formula, we’d be in for a surprise:> plot(weight ~ height^2, data=kid.weights) # not asexpected> res = lm(weight ~ height^2, data=kid.weights)> abline(res)The resulting graph would look identical to the graph of height versus weight in Figure3.8 and not the graph of height squared versus weight in Figure 3.12.The reason for this is that the model formula syntax uses the familiar math notations *,/, ^ differently. To use them in their ordinary sense, we need to insulate them in theformulas with the I() function, as in: