# Should control variables be included in model if statistically insignificant?

I have a set of predictors in a linear regression, as well as three control variables. The issue here is that one of my variables of interest is only statistically significant if the control variables are included in the final model. However, the control variables themselves are not statistically significant.

Here is how the multicollinearity of all my variables look like (including control variables):

 > vif(lm(return ~ EQ + EFF + SIZE + MOM + MSCR + UMP, data = as.data.frame(port.df)))
EQ      EFF     SIZE      MOM     MSCR      UMP
3.687171 3.481672 2.781901 1.064312 1.438596 1.003408

> vif(lm(return ~ EQ + MOM + MSCR, data = as.data.frame(port.df)))
EQ      MOM     MSCR
1.359992 1.048142 1.412658


My variables of interest are EQ, MOM and MSCR, and the control variables are EFF, SIZE and UMP. EQ is only significant if the three control var are included, and becomes insignificant when they are not:

• Here are the coefficients (1rst row) and t-stats (2nd row) when control variables are included (notice that EQ is statistically significant)

       intercept           EQ          EFF        SIZE         MOM       MSCR          UMP
[1,] 0.005206246 -0.006310531 0.0001229055 0.004125551 0.007738259 0.00473377 5.838596e-06
[2,] 1.866628909 -1.746583234 0.0388823612 1.178460997 2.145062820 2.08131100 1.994863e-01

• Now, here is the result of the regression when the control variables are excluded (notice that EQ is NOT statistically significant anymore)

       intercept           EQ         MOM       MSCR
[1,] 0.007313402 -0.002111833 0.007128606 0.00668364
[2,] 2.652662996 -0.595391117 2.036985378 2.80177366


The problem is that when I include my control variables, all my variables of interest are significant, but my control variables are not.

Which variables should I include in my final model? How should I structure my final model then, given the fact that the model will be used for forecasting?

Thank you,

• Why are some variables "of interest" & some "control"? That is, if the point of the model's to forecast, why aren't they on an equal footing? Will some not be available for forecasting purposes? Sep 6, 2013 at 14:31
• They will all be available for forecasting purposes. Should I then consider them all "of interest"? If that's the case, how would I deal with the fact that 3 of them are insignificant, but their presence affects the significance of another variable? Sep 6, 2013 at 14:33
• While there may be a distinction between control and other variables in your mind, it is vital to realise that neither the statistics nor the software pays any attention to that distinction. Sep 6, 2013 at 14:39
• True that. The question remains that even assuming all of these variables are "of interest", how should I structure my final model given the statistical significance shown above (that depends on which variables are included)? Sep 6, 2013 at 14:43
• Just read up on LASSO again & forget about "significance". This is like a doctor asking how many leeches to apply after a course of antibiotics. Sep 6, 2013 at 15:14