Yes, because:

(i) you deliberately used these variables to built the model, so it should be shown what their contribution to the reduction of the residual variance is, and

(ii) their consideration in the model can impact the contribution of other variables in the model (because of co-linearities).

Note that "insignificant (p>0.05)" does NOT imply irrelevance!

(and that "significant (p

Yes, because:

(i) you deliberately used these variables to built the model, so it should be shown what their contribution to the reduction of the residual variance is, and

(ii) their consideration in the model can impact the contribution of other variables in the model (because of co-linearities).

Note that "insignificant (p>0.05)" does NOT imply irrelevance!

(and that "significant (p

Adding to Jochen's good comments, when one sees a model with sample size < HUGE and all variables being statistically significant, it is a sign that suggests over-fitting of the model (by removal of any non-significant terms).  See the section headed "Lack of insignificant variables in the final model" in the author checklist linked below.  HTH.

http://biostat.mc.vanderbilt.edu/wiki/Main/ManuscriptChecklist

In addition to Jochen's and Bruce's comments, Yes...if a variable was used to fit  the model, it should be included in the final mathematical model. If you ran several models (that used varied combinations of variables, which could have resulted from addition or exclusion of some variables), and ended up selecting a certain model, explain the criteria used to select that particular model and why the variables (if any) were excluded. Were they not improving the model? Were they not contributing much to the model (When you use step-wise regression)

My special thanks to Jochen Wilhelm, Bruce Weaver, Dorcas Kareithi for your kind response.