THE CHOW TEST is a widely used procedure for testing for the equality of sets of coefficients in two linear regression models. However, when the number of observations in one of the models is less than the number of regression coefficients, the Chow test is incapable of testing the hypothesis of equality against that of inequality. It can never be concluded from the Chow test itself that the two sets are equal, although at times it may be possible to conclude that they are unequal. This point is implicit in [1], but has not been specifically discussed heretofore. The indeterminacy of the Chow test results from the insufficient number of observations. The two linear regression models, each of which is assumed to satisfy the conditions of the standard normal linear regression model, can be written as