I run a regression for my study. I used a quarterly data included 33 number of observations. my problem is independent variables are significant but not perfectly significant. when i run a multicollinearity, 2 of independent variables ,multicollinearity. so i exclude those two variables. and run a second model with only the significant variables. however, then my second model shows another independent variables as insignificant, while previous result it is shows a significant at 5% level. Sorry i don't know how to explain. hope you guys get what I am trying to solve. It really stress thinking the solutions. this is my result. I change the unit to % using formula 100*dlog(x). I am really thankful for any reply.
I would certainly have expected that we already had a question on "why do $p$ values change if I change my model", but apparently we don't. So, here goes:
Remember how $p$ values and significance are calculated in regression:
- You estimate coefficients
- You estimate the standard errors of these coefficients
- You divide the absolute values of the coefficients by the corresponding standard error to obtain $t$ statistics
- You look up the $p$ value corresponding to your $t$ statistics
Now, if you change your model - by adding, deleting or transforming predictors - the first two calculations will change, because both a regressor's coefficient estimate and its standard error estimate are calculated in the context of the whole model.
And since the first two calculations change, which are the inputs to the last two steps, the final $p$ value will also change.
Different model $\longrightarrow$ different estimates $\longrightarrow$ different $p$ values.
And there is no reason why a $p<0.05$ for a given coefficient estimate before your model change should still be $<0.05$ after your model change.
So: everything works as it should. You will still need to interpret your results in the light of your theory.
Incidentally, what you are doing is called stepwise-regression (I have added the tag). It is not good practice in inferential statistics, since $p$ values calculated after stepwise regression are invalid.