Abstract: This paper examines the goodness-of-fit of a polynomial regression model. We derive the asymptotic distribution of two generalizations of the classical F test by means of spline estimators. Furthermore, we propose an analysis of variance technique that extends the classical one from linear to nonparametric regression, and we put forward a coefficient of determination for nonparametric models.
Key words and phrases: Analysis of variance, goodness of fit, hypothesis testing, multiple determination coefficient, nonparametric estimation.