The Student's t Test in Multiple Regression under Simple Collinearity

This paper is concerned with the validity of the conventional t tests on regression coefficients when there is serious multicollinearity between the explanatory variables. It is well known that increasing multicollinearity causes the true standard errors of regression coefficients to rise. The crucial question, however, is whether the conventional formulas will in practice reflect this rise. The purpose of this note is to show that the conventional t tests will in practice reflect this rise. But this note also points out the danger involved in mechanically dropping variables from multiple regression equations by t tests because t values of the regression coefficients may not be significantly different from zero when the true (population) values of these coefficients are in fact not zero, if the explanatory variables are highly intercorrelated.