Nonparametric Regression

An important question in many fields of science is the relationship between two variables, say X and Y. Regression analysis is concerned with the question of how Y (the dependent variable) can be explained by X (the independent or explanatory or regressor variable). This means a relation of the form $$ Y = m(X) $$, where m(●) is a function in the mathematical sense. In many cases theory does not put any restrictions on the form of m(●), i.e. theory does not say whether m(●) is linear, quadratic, increasing in X , etc.. Hence, it is up to empirical analysis to use data to find out more about m(●).