On the significance level of the multirelation coefficient

The concept of the multirelation coe cient is de ned 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 signi cance levels of the multirelation coe cient for any given number of observations and variables A generalized Student t distribution is de ned 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 signi cance level of the multirelation coe cient