Selecting regression variables
I am building a regression model to predict housing price, and so far I have 6 variables in the model, and they are all statistically significant, two of them are as follows:
Then I added the interaction variable (x1x2) between x1 and x2, and the results are as follows:
As you can see, there is a significant interaction between x1 and x2. However, x1 and x2 alone are no longer significant!
One testbook suggested that whenever we use an interaction variable, we also include the explanatory variables involved (x1 and x2 in this case). However, in my case, x1 and x2 is not significant.
Therefore, what should I do?
1. Use only x1 and x2 in the model?
2. Use x1, x2, and x1x2 in the model?
3. Use only x1x2 in the model?
Please explain the reason of your suggestion.
Thanks a lot.