Nonparametric Goodness of Fit Test for Regression Using Local Residuals by Neighbor Join Methods

Since Sir Francis Galton presented his rudimentary idea of regression line in 1877, regression analysis has become a center of statistical analysis in both observational studies and experimental studies. With the advance of computational environment, more generalized and sophisticated models than simple linear regression, such as multivariate, polynomial, exponential, logistic, time-series, semi-parametric (Proportional Hazards Regression) and general nonlinear regression, were encompassed. It is because regression analysis provides the conceptual simplicity of using an equation to represent a relationship between predictor variables and their associated response. (1) However, as much as attractive it is, regression can be easily misused. Regression which is the core of parametric methods builds upon certain underlying assumptions even in its most general form. Therefore, any regression model cannot be validated unless reasonable satisfaction of those assumptions.