A Note on the Role of Independence in t Statistics Constructed From Linear Statistics in Regression Models

Abstract

Some Studentized linear estimates do not follow Student's t distributions because the numerator and denominator are not independent. Recognized in residuals, the problem can occur in other contexts as well. A remedy is easily obtained by adding another predictor variable to the regression model that removes the shared degree of freedom.

Key Words:

• Nonorthogonality
• Restricted least squares
• Test statistics in regression