Modelling Maximum Oxygen Uptake — a Case‐Study in Nonlinear Regression Model Formulation and Comparison

This case‐study outlines the important stages that needed to be addressed when formulating a regression model to explain health‐related variables, such as maximum oxygen uptake, taken from the Allied Dunbar national fitness survey. Relevant references suggested two competing models. A nonlinear regression model, originally proposed to predict forced expiratory volume, appeared to be equally suitable for predicting the estimated maximum oxygen uptake. However, the parsimonious solution was found to be inexplicable on physiological grounds, as well as providing heteroscedastic and non‐normal residuals. An alternative weighted log‐linear regression model, containing a proportional body weight and a negative exponential age term, was then considered. This model gave more plausible and precise parameter estimates which had a generally lower level of intercorrelation. The log‐linear model also gave less evidence of multicollinearity and the residuals were found to be acceptably normal. Finally, a bootstrap comparison of likelihoods confirmed the log‐linear model to be superior.