Farrar-Glauber Test

The Farrar-Glauber test is a collection of tests for detecting multicollinearity among the explanatory variables in a linear regression. If is their sample correlation matrix, is the number of observations, and is the number of explanatory variables, its overall test statistic is

Under the null hypothesis that the explanatory variables are mutually uncorrelated, this statistic is approximately chi-squared distributed with degrees of freedom. Farrar and Glauber also gave tests based on the matrix inverse of the correlation matrix for individual variables and on correlations between variable pairs after the remaining variables have been accounted for. The procedure is primarily diagnostic: rejection indicates collinearity but does not identify a unique remedy.