Modelling Maximum Oxygen Uptake-A Case-Study in Non-Linear Regression Model Formulation and Comparison
通过英国全国健身调查数据，比较了两种回归模型在预测最大摄氧量上的表现，发现加权对数线性模型优于非线性模型。
SUMMARY 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 non-linear 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.