I have 2 Multiple Linear Regression models. One with all 7 predictors, and the other with 2 predictors (the other 5 insignificant ones removed). I have to compare these two models. What would be an appropriate test to do this?
1. In terms of hypothesis testing. Since these are nested models, you can run a test on whether the model with the extra covariates fits the data better than the more simple models with less variables. This would involve an exact F test or a chi-square test based on the asymptotics of the likelihood function.
2. If the interest is on predictions, you could check which model gives better predictions on the training data or in a subset of the data (basically cross validation).