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(X(i1); X(i2);...; X(im)) holds for some function f, where 1 less than or equal to i(1) < i(2) <... i(m) less than or equal to k, and X(1);...; X(k) 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 (X(i1); X(i2);...; X(im)). Using the dependency statistic delta(Y,(Xi1;...; Xim))(j), 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 X(i1);...; X(im) among the random variables X(1); X(2);...; X(k), which better explain Y.