I have a set of data containing 4 predictors (environmental conditions and animal size) and one predicted variable (animal growth rate). I want to fit a regression model to this data. I have two objectives:
Test the importance and interactions between predictors. I am most interested in interactions between size and other predictors, as I have some clue that animal should change its reactions to environmental factors as it grows. But other interactions may be interesting as well and I am not sure if I can (or should) just drop some interactions from the model. I want to test it using t-test for coefficients (calculated automatically in R with the model fit).
Select the best model for future predictions. To do this I want to use AIC or BIC criterion to all possible submodels, as the number of combinations is not so big.
The question is:
Should I perform t-test after or before model selection? The two mentioned objectives are more or less independent as the first one is just theoretical insight and the second is more practical. This suggests that I should perform t-test on full model and model selection afterwards. But I am not sure.