I came across a result today stating that if the coefficient of the highest order of independent variable in the regression equation comes out to be necessary (via hypothesis testing), then the lower order terms of the independent variable are also necessary.

Can anyone explain to me why this should happen?

To put it more simply, if the regression equation is:

$Y= A +B*X +C*X^2$

Then, I should first test for C=0 and if this is not the case, then need not check for B=0. I wanted to know why should this always be the case? I am a newbie to this and sorry if this is a silly question, but I simply could not take it for granted.

  • $\begingroup$ Where did you come across this "result"? $\endgroup$ – Mark L. Stone Jan 19 '16 at 1:11
  • $\begingroup$ I think you may be confused. Multiple tests used in regression analysis would be substantially simplified if this result held. E.g. Ramsey RESET test or White test of homoskecasticity of residuals - they all test significance of vatiables with high and low powers - not only significance of high powers. $\endgroup$ – DatamineR Jan 19 '16 at 1:40