In univariate case, general measure of the degree of dependency of one variable on another is a correlation ratio. In multivariate setup earlier it was defined such through trace of conditional covariance matrix of a sub-vector given the other sub-vector divided by the trace of the variance-covariance matrix of the former and also obtained some results on such measure for predictability. But more appropriate generalization of such measure is defined here through eigenvalues of the dispersion matrix of the predictor relative to whole dispersion matrix. Then it is applied to see how far physiological variables depend on anthropometric variables. It is found that chosen physiological variables have higher degree of dependency on the selected anthropometric variables.
Key words: Correlation Ratio; Measure of Predictability; AMS Classification: 62H, 62P. Corresponding Author
: Babulal Seal*