We introduce and study a new type of regression that arises from a kinesiology experiment concerning human's tolerance to temperature and water vapor pressure. In the experiment, a set of pressure and temperature values are collected to construct a psychrometric chart. The problem differs from traditional regression because, for one part of the data, temperature is held fixed while pressure is raised to an equilibrium point; for the other part of the data, pressure is held fixed while temperature is raised to an equilibrium point. The purpose of this peculiar design is to ensure the safety of the participants. Traditional regression is inadequate for modeling this type of data, because the roles of predictor and response alternate. We propose a new regression where the predictor and response alternate while being linked by a bijective function. We study the population and asymptotic properties of this regression, develop test statistics for model selection and analysis of variance, and outline several extensions and refinements. We apply the method to kinesiology data and find, among other things, that the gender difference in psychrometric charts diminishes in old age.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty