#### Article Title

#### Abstract

Consider three random variables *Y*, *X*_{1} and *X*_{2}, where the typical value of *Y*, given *X*_{1} and *X*_{2}, is given by some unknown function *m*(*X*_{1}, *X*_{2}). A goal is to determine which of the two independent variables is most important when both variables are included in the model. Let *τ*_{1} denote the strength of the association associated with *Y* and *X*_{1}, when *X*_{2} is included in the model, and let *τ*_{2} be defined in an analogous manner. If it is assumed that *m*(*X*_{1}, *X*_{2}) is given by *Y* = *β*_{0} + *β*_{1}*X*_{1} + *β*_{2}*X*_{2} for some unknown parameters *β*_{0}, *β*_{1} and *β*_{2}, a robust method for testing H_{0} : *τ*_{1} = *τ*_{2} is now available. However, the usual linear model might not provide an adequate approximation of the regression surface. Many smoothers (nonparametric regression estimators) were proposed for estimating the regression surface in a more flexible manner. A robust method is proposed for assessing the strength of the empirical evidence that a decision can be made about which independent variable is most important when using a smoother. The focus is on LOESS, but it is readily extended to any nonparametric regression estimator of interest.

#### DOI

10.22237/jmasm/1525132920

#### Recommended Citation

Wilcox, R. (2018). An Inferential Method for Determining Which of Two Independent Variables Is Most Important When There Is Curvature. Journal of Modern Applied Statistical Methods, 17(1), eP2588. doi: 10.22237/jmasm/1525132920

#### Included in

Applied Statistics Commons, Social and Behavioral Sciences Commons, Statistical Theory Commons