1 - Introduction

Summary

As regards problems of specification, these are entirely a matter for the practical statistician, for those cases where the qualitative nature of the hypothetical population is known do not involve any problems of this type.

Sir R. A. Fisher (1922)

A regression curve describes a general relationship between an explanatory variable X and a response variable Y. Having observed X , the average value of Y is given by the regression function. It is of great interest to have some knowledge about this relation. The form of the regression function may tell us where higher Y -observations are to be expected for certain values of X or whether a special sort of dependence between the two variables is indicated. Interesting special features are, for instance, monotonicity or unimodality. Other characteristics include the location of zeros or the size of extrema. Also, quite often the regression curve itself is not the target of interest but rather derivatives of it or other functionals.