The geometrical interpretation of statistical tests in multivariate linear regression

摘要

A geometrical interpretation of the classical tests of the relation between two sets of variables is presented. One of the variable sets may be considered as fixed and then we have a multivariate regression model. When the Wilks' lambda distribution is viewed geometrically it is obvious that the two special cases, the F distribution and the Hotelling T2 distribution are equivalent. From the geometrical perspective it is also obvious that the test statistic and the p-value are unchanged if the responses and the predictors are interchanged.