Practical Significance Ranking of Regressors and Exact t Density

Consider a possibly nonlinear nonparametric regression with p regressors. We provide evaluations by 13 methods to rank regressors by their practical significance or importance using various methods, including machine learning tools. Comprehensive methods are as follows. m6=Generalized partial correlation coefficient or GPCC by Vinod (2021) and Vinod (2022)< https://www.mdpi.com/1911-8074/15/1/32>. m7= a generalization of psychologists' effect size incorporating nonlinearity and many variables. m8= local linear partial (dy/dxi) using the 'np' package for kernel regressions. m9= partial (dy/dxi) using the 'NNS' package. m10= importance measure using the 'NNS' boost function. m11= Shapley Value measure of importance (cooperative game theory). m12 and m13= two versions of the random forest algorithm. Taraldsen's exact density for sampling distribution of correlations added.