Regression analysis and dependence

In this paper we study the relationship between regression analysis and a multivariate dependency measure. If the general regression model Y=f([inline-graphic not available: see fulltext]) holds for some function f, where 1≤i1< i2<···im ≤k, and X1,...,Xk is a set of possible explanatory random variables for Y. Then there exists a dependency relation between the random variable Y and the random vector ([inline-graphic not available: see fulltext]). Using the dependency statistic [inline-graphic not available: see fulltext] defined below, we can detect such dependency even if the function f is not linear. We present several examples with real and simulated data to illustrate this assertion. We also present a way to select the appropriate subset [inline-graphic not available: see fulltext] among the random variables X1,X2,...,Xk, which better explain Y.