Hi, I am not sure that I totally understand the models you build. Could you give a brief description of your problem, variables? And also your models respectively with and without this dummy variable? How did you compare the performance of these two models (metric, statistic test)?

Mohamed Hashem -

I would not pay much attention to "significance." Size effect matters.

I suggest you try a "graphical residual analysis" with and without this variable, on the same scatterplot, for the same sample. This could be enlightening. You also could consider a cross-validation, as results could be different for a different sample.

If you still have questions, I suggest that you post your graphical residual analysis or analyses.

Cheers - Jim

PS -

I wonder if that dummy intercept variable may really not be useful, and just a way to make a model 'fit' to a sample. This can happen, especially if the sample size is too small. Consider this: If all predictors were zero, would you expect y to be zero? If so, do not include an intercept term. It is just a reaction to random 'error.' (On page 110 in Brewer, K.R.W.(2002), Combined Survey Sampling Inference: Weighing Basu's Elephants, Arnold: London and Oxford University Press, Ken Brewer provides a warning about intercept terms which may not be needed.) If you don't need it in any case, you should probably drop it, I think.

Dear,

You can check this file, it could help you:

https://gargicollege.in/wp-content/uploads/2020/03/Dummy-Variables-Econometrics.pdf