If X^2 is not significant but X is significant, do I have to remove X^2 and run again the regression analysis? Model DV ~ W+PDSR+Corr+(FAGDP1+FAGDP2)+log(PCGDP)+Exp+Pop+Health
FAGDP2=FAGDP1^2
Result:
After removing FAGDP2(FAGDP1^2) from the model, FAGDP1 turns to be insignificant

Am I right in removing FAGDP^2 ?

Quite generally, insignificant variables do not have to be removed from regression models (this also holds for parameters belonging to terms such as $X^2$). Also, generally, standard regression tests are invalid in models that stem from data driven selection.
