On the significance level of the multirelation coefficient

The concept of the multirelation coefficient is defined to describe the closeness of a set of variables to a linear relation. This concept extends the linear correlation between two variables to two or more variables. Parameters of a beta distribution are determined that are utilized to approximate significance levels of the multirelation coefficient for any given number of observations and variables. A generalized Student t distribution is defined. This distribution, which is termed the multirelated t distribution, reduces to the Student t distribution for two variables. It is useful in the determination of the significance level of the multirelation coefficient.